研究者詳細 - 曽我部　知広

論文 - 曽我部　知広

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A preconditioning technique of Gauss-Legendre quadrature for the logarithm of symmetric positive definite matrices Open Access

Tatsuoka, F; Sogabe, T; Kemmochi, T; Zhang, SL

APPLIED MATHEMATICS LETTERS 167 巻頁： 109552 - 109552 2025年8月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Applied Mathematics Letters

This note considers the computation of the logarithm of symmetric positive definite matrices using the Gauss–Legendre (GL) quadrature. The GL quadrature becomes slow when the condition number of the given matrix is large. In this note, we propose a technique dividing the matrix logarithm into two matrix logarithms, where the condition numbers of the divided logarithm arguments are smaller than that of the original matrix. Although the matrix logarithm needs to be computed twice, each computation can be performed more efficiently, and it potentially reduces the overall computational cost. It is shown that the proposed technique is effective when the condition number of the given matrix is approximately between 130 and 3.0×105.

DOI： 10.1016/j.aml.2025.109552

Web of Science

Scopus

A tensor Alternating Anderson-Richardson method for solving multilinear systems with M-tensors 査読有り

Niu, J; Du, L; Sogabe, T; Zhang, SL

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 461 巻 2025年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Computational and Applied Mathematics

It is well-known that a multilinear system with a nonsingular M-tensor and a positive right-hand side has a unique positive solution. Tensor splitting methods generalizing the classical iterative methods for linear systems have been proposed for finding the unique positive solution. The Alternating Anderson–Richardson (AAR) method is an effective method to accelerate the classical iterative methods. In this study, we apply the idea of AAR for finding the unique positive solution quickly. We first present a tensor Richardson method based on tensor regular splittings, then apply Anderson acceleration to the tensor Richardson method and derive a tensor Anderson–Richardson method, finally, we periodically employ the tensor Anderson–Richardson method within the tensor Richardson method and propose a tensor AAR method. Numerical experiments show that the proposed method is effective in accelerating tensor splitting methods.

DOI： 10.1016/j.cam.2024.116419

Web of Science

Scopus

電磁界解析の複素対称行列向け積型反復法査読有り

杉本振一郎，曽我部知広，張紹良，荻野正雄，武居周

電気学会論文誌 145 巻 ( 2 ) 頁： 87 - 97 2025年2月

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：IEEJ Transactions on Industry Applications

This paper deals with time-harmonic problems with complex symmetric matrices in the electromagnetic field analysis. To solve such problems more stably and quickly, the Product-type Krylov Subspace Methods based on the COCG and COCR methods are proposed, and verified in finite element analyses of the time-harmonic eddy current and high-frequency electromagnetic field problems. As a result, in some cases, the number of iterations and the computational time have been reduced.

DOI： 10.1541/ieejias.145.87

Scopus

CiNii Research

Computing the matrix exponential with the double exponential formula 査読有り

Tatsuoka, F; Sogabe, T; Kemmochi, T; Zhang, SL

SPECIAL MATRICES 12 巻 ( 1 ) 2024年10月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Special Matrices

This article considers the computation of the matrix exponential eA with numerical quadrature. Although several quadrature-based algorithms have been proposed, they focus on (near) Hermitian matrices. In order to deal with non-Hermitian matrices, we use another integral representation including an oscillatory term and consider applying the double exponential (DE) formula specialized to Fourier integrals. The DE formula transforms the given integral into another integral whose interval is infinite, and therefore, it is necessary to truncate the infinite interval. In this article, to utilize the DE formula, we analyze the truncation error and propose two algorithms. The first one approximates eA with the fixed mesh size, which is a parameter in the DE formula affecting the accuracy. The second one computes eA based on the first one with automatic selection of the mesh size depending on the given error tolerance.

DOI： 10.1515/spma-2024-0013

Web of Science

Scopus

Adaptive projected SOR algorithms for nonnegative quadratic programming 査読有り Open Access

Miyatake, Y; Sogabe, T

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2024年10月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Japan Journal of Industrial and Applied Mathematics

The choice of relaxation parameter in the projected successive overrelaxation (PSOR) method for nonnegative quadratic programming problems is problem-dependent. We present novel adaptive PSOR algorithms that adaptively control the relaxation parameter using the Wolfe conditions. The method and its variants can be applied to various problems without requiring additional assumptions, barring the positive semidefiniteness concerning the matrix that defines the objective function, and the cost for updating the parameter is negligible in the whole iteration. Numerical experiments show that the proposed methods often perform comparably to (or sometimes superior to) the PSOR method with a nearly optimal relaxation parameter.

DOI： 10.1007/s13160-024-00672-4

Web of Science

Scopus

Matrix equation representation of the convolution equation and its unique solvability 査読有り

Satake, Y; Sogabe, T; Kemmochi, T; Zhang, SL

SPECIAL MATRICES 12 巻 ( 1 ) 2024年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Special Matrices

We consider the convolution equation F ∗ X = B F∗ X=B, where F ϵ ℝ3 × 3 and B ϵ ℝm × n are given and X ϵ ℝm × n is to be determined. The convolution equation can be regarded as a linear system with a coefficient matrix of special structure. This fact has led to many studies including efficient numerical algorithms for solving the convolution equation. In this study, we show that the convolution equation can be represented as a generalized Sylvester equation. Furthermore, for some realistic examples arising from image processing, we show that the generalized Sylvester equation can be reduced to a simpler form, and we analyze the unique solvability of the convolution equation.

DOI： 10.1515/spma-2024-0001

Web of Science

Scopus

その他リンク： https://www.degruyter.com/document/doi/10.1515/spma-2024-0001/pdf

Shifted LOPBiCG: A locally orthogonal product-type method for solving nonsymmetric shifted linear systems based on Bi-CGSTAB 査読有り

Zhao, RJ; Sogabe, T; Kemmochi, T; Zhang, SL

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 31 巻 ( 2 ) 2024年3月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Numerical Linear Algebra with Applications

When solving shifted linear systems using shifted Krylov subspace methods, selecting a seed system is necessary, and an unsuitable seed may result in many shifted systems being unsolved. To avoid this problem, a seed-switching technique has been proposed to help switch the seed system to another linear system as a new seed system without losing the dimension of the constructed Krylov subspace. Nevertheless, this technique requires collinear residual vectors when applying Krylov subspace methods to the seed and shifted systems. Since the product-type shifted Krylov subspace methods cannot provide such collinearity, these methods cannot use this technique. In this article, we propose a variant of the shifted BiCGstab method, which possesses the collinearity of residuals, and apply the seed-switching technique to it. Some numerical experiments show that the problem of choosing the initial seed system is circumvented.

DOI： 10.1002/nla.2538

Web of Science

Scopus

Tensor product-type methods for solving Sylvester tensor equations 査読有り

Niu Jing, Sogabe Tomohiro, Du Lei, Kemmochi Tomoya, Zhang Shao-Liang

APPLIED MATHEMATICS AND COMPUTATION 457 巻 2023年11月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Applied Mathematics and Computation

The tensor biconjugate gradient (TBiCG) method has recently been proposed for solving Sylvester tensor equations. The TBiCG method is based on the BiCG method that may exhibit irregular convergence behavior. To overcome the limitations, product-type methods, such as BiCGSTAB and GPBiCG, have been proposed. In this study, we apply the idea of product-type methods to solve Sylvester tensor equations and propose tensor GPBiCG and BiCGSTAB methods. Furthermore, we consider preconditioned algorithms of the tensor GPBiCG and BiCGSTAB methods using the nearest Kronecker product preconditioner. Numerical experiments illustrate that the proposed methods are competitive with some existing methods.

DOI： 10.1016/j.amc.2023.128155

Web of Science

Scopus

QUANTUM ALGORITHMS BASED ON THE BLOCK-ENCODING FRAMEWORK FOR MATRIX FUNCTIONS BY CONTOUR INTEGRALS 査読有り国際誌

Takahira S., Ohashi A., Sogabe T., Usuda T.S.

Quantum Information and Computation 22 巻 ( 11&12 ) 頁： 965 - 979 2022年8月

掲載種別：研究論文（学術雑誌）出版者・発行元：Quantum Information and Computation

The matrix functions can be defined by Cauchy’s integral formula and can be approx-imated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we propose a quantum algorithm for matrix functions based on a procedure to implement the linear combination of the inverses on quantum computers. Compared with the previous study [S. Takahira, A. Ohashi, T. Sogabe, and T.S. Usuda, Quant. Inf. Comput., 20, 1&2, 14-36, (Feb. 2020)] that proposed a quantum algorithm to compute a quantum state for the matrix function based on the circular contour cen- tered at the origin, the quantum algorithm in the present paper can be applied to a more general contour. Moreover, the algorithm is described by the block-encoding framework. Similarly to the previous study, the algorithm can be applied even if the input matrix is not a Hermitian or normal matrix. This is an advantage compared with quantum singular value transformation.

DOI： 10.26421/qic22.11-12-4

Scopus

Recent development for computing singular values of a generalized tensor sum 査読有り

Ohashi Asuka, Sogabe Tomohiro

Journal of Advanced Simulation in Science and Engineering 9 巻 ( 1 ) 頁： 136 - 149 2022年

Numerical Algorithms for Computing an Arbitrary Singular Value of a Tensor Sum 査読有り

Ohashi Asuka, Sogabe Tomohiro

AXIOMS 10 巻 ( 3 ) 2021年9月

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：Axioms

We consider computing an arbitrary singular value of a tensor sum: (Formula presented). We focus on the shift-and-invert Lanczos method, which solves a shift-and-invert eigenvalue problem of (TT T − ˜σ2 Iℓmn)−1, where ˜σ is set to a scalar value close to the desired singular value. The desired singular value is computed by the maximum eigenvalue of the eigenvalue problem. This shift-and-invert Lanczos method needs to solve large-scale linear systems with the coefficient matrix TT T − ˜σ2 Iℓmn. The preconditioned conjugate gradient (PCG) method is applied since the direct methods cannot be applied due to the nonzero structure of the coefficient matrix. However, it is difficult in terms of memory requirements to simply implement the shift-and-invert Lanczos and the PCG methods since the size of T grows rapidly by the sizes of A, B, and C. In this paper, we present the following two techniques: (1) efficient implementations of the shift-and-invert Lanczos method for the eigenvalue problem of TT T and the PCG method for TT T − ˜σ2 Iℓmn using three-dimensional arrays (third-order tensors) and the n-mode products, and (2) preconditioning matrices of the PCG method based on the eigenvalue and the Schur decomposition of T. Finally, we show the effectiveness of the proposed methods through numerical experiments.

DOI： 10.3390/axioms10030211

Web of Science

Scopus

A thick-restart Lanczos type method for HermitianJ-symmetric eigenvalue problems 査読有り

Ishikawa Ken-Ichi, Sogabe Tomohiro

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 38 巻 ( 1 ) 頁： 233 - 256 2021年2月

K omega - Open-source library for the shifted Krylov subspace method of the form(zI - H)x = b 査読有り

Hoshi Takeo, Kawamura Mitsuaki, Yoshimi Kazuyoshi, Motoyama Yuichi, Misawa Takahiro, Yamaji Youhei, Todo Synge, Kawashima Naoki, Sogabe Tomohiro

COMPUTER PHYSICS COMMUNICATIONS 258 巻 2021年1月

Computing the matrix fractional power with the double exponential formula 査読有り

Tatsuoka F., Sogabe T., Miyatake Y., Kemmochi T., Zhang S.L.

Electronic Transactions on Numerical Analysis 54 巻頁： 558 - 580 2021年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：Electronic Transactions on Numerical Analysis

Two quadrature-based algorithms for computing the matrix fractional power Aα are presented in this paper. These algorithms are based on the double exponential (DE) formula, which is well-known for its effectiveness in computing improper integrals as well as in treating nearly arbitrary endpoint singularities. The DE formula transforms a given integral into another integral that is suited for the trapezoidal rule; in this process, the integral interval is transformed into an infinite interval. Therefore, it is necessary to truncate the infinite interval to an appropriate finite interval. In this paper, a truncation method, which is based on a truncation error analysis specialized to the computation of Aα, is proposed. Then, two algorithms are presented-one where Aα is computed with a fixed number of abscissa points and one with Aα computed adaptively. Subsequently, the convergence rate of the DE formula for Hermitian positive definite matrices is analyzed. The convergence rate analysis shows that the DE formula converges faster than Gaussian quadrature when A is ill-conditioned and α is a non-unit fraction. Numerical results show that our algorithms achieve the required accuracy and are faster than other algorithms in several situations.

DOI： 10.1553/0X003CC757

Scopus

On a transformation of the (*)-congruence Sylvester equation for the least squares optimization 査読有り

Satake Yuki, Sogabe Tomohiro, Kemmochi Tomoya, Zhang Shao-Liang

OPTIMIZATION METHODS & SOFTWARE 35 巻 ( 5 ) 頁： 974 - 981 2020年9月

Algorithms for the computation of the matrix logarithm based on the double exponential formula 査読有り

Tatsuoka Fuminori, Sogabe Tomohiro, Miyatake Yuto, Zhang Shao-Liang

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 373 巻 2020年8月

Generalized Sherman-Morrison-Woodbury formula based algorithm for the inverses of opposite-bordered tridiagonal matrices 査読有り

Jia Ji-Teng, Sogabe Tomohiro

JOURNAL OF MATHEMATICAL CHEMISTRY 58 巻 ( 7 ) 頁： 1466 - 1480 2020年8月

Adaptive SOR methods based on the Wolfe conditions 査読有り

Miyatake Yuto, Sogabe Tomohiro, Zhang Shao-Liang

NUMERICAL ALGORITHMS 84 巻 ( 1 ) 頁： 117 - 132 2020年5月

An Implicit Evaluation Method of Vector 2-Norms Arising from Sphere Constrained Quadratic Optimizations 招待有り査読有り

Sogabe T., Suzuki A., Zhang S-L

CSIAM TRANSACTIONS ON APPLIED MATHEMATICS 1 巻 ( 1 ) 頁： 142 - 154 2020年3月

QUANTUM ALGORITHM FOR MATRIX FUNCTIONS BY CAUCHY'S INTEGRAL FORMULA 査読有り

Takahira Souichi, Ohashi Asuka, Sogabe Tomohiro, Usuda Tsuyoshi Sasaki

QUANTUM INFORMATION & COMPUTATION 20 巻 ( 1-2 ) 頁： 14 - 36 2020年2月

Relation between the T-congruence Sylvester equation and the generalized Sylvester equation 査読有り

Satake Yuki, Oozawa Masaya, Sogabe Tomohiro, Miyatake Yuto, Kemmochi Tomoya, Zhang Shao-Liang

APPLIED MATHEMATICS LETTERS 96 巻頁： 7 - 13 2019年10月

Bidiagonalization of (k, k + 1)-tridiagonal matrices 査読有り

Takahira S., Sogabe T., Usuda T. S.

SPECIAL MATRICES 7 巻 ( 1 ) 頁： 20-26 2019年1月

On computing the minimum singular value of a tensor sum 査読有り

Ohashi A., Sogabe T.

SPECIAL MATRICES 7 巻 ( 1 ) 頁： 95 - 106 2019年1月

A structure-preserving fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear schrödinger equation 査読有り

Miyatake Y.

Journal of Computational Dynamics 6 巻 ( 2 ) 頁： 361 - 383 2019年

指定番目の特異値と特異ベクトルの計算について査読有り

Lee Dongjin, 曽我部知広, 宮武勇登, Zhang Shao-Liang

日本応用数理学会論文誌(Web) 29 巻 ( 1 ) 頁： 121‐140(J‐STAGE) - 140 2019年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本応用数理学会

概要. 本論文では，大規模疎行列の指定番目の特異値と特異ベクトルの計算問題に対するアルゴリズムを提案する．提案アルゴリズムでは対象問題をいくつかの小問題に分け，各小問題において特異値問題と等価な固有値問題を解く．数値実験では提案アルゴリズムの計算精度を確認し，大規模行列に対する有効性について検討する．

DOI： 10.11540/jsiamt.29.1_121

J-GLOBAL

Modified Strang splitting for semilinear parabolic problems 査読有り

Nakano Kosuke, Kemmochi Tomoya, Miyatake Yuto, Sogabe Tomohiro, Zhang Shao-Liang

JSIAM Letters 11 巻 ( 0 ) 頁： 77 - 80 2019年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本応用数理学会

We consider applying the Strang splitting to semilinear parabolic problems. The key ingredients of the Strang splitting are the decomposition of the equation into several parts and the computation of approximate solutions by combining the time evolution of each split equation. However, when the Dirichlet boundary condition is imposed, order reduction could occur due to the incompatibility of the split equations with the boundary condition. In this paper, to overcome the order reduction, a modified Strang splitting procedure is presented for the one-dimensional semilinear parabolic equation with first-order spatial derivatives, like the Burgers equation.

DOI： 10.14495/jsiaml.11.77

Web of Science

On the equivalence between SOR-type methods for linear systems and the discrete gradient methods for gradient systems 査読有り

Miyatake Yuto, Sogabe Tomohiro, Zhang Shao-Liang

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 342 巻頁： 58-69 2018年11月

Solution of the k-th eigenvalue problem in large-scale electronic structure calculations 査読有り

Lee Dongjin, Hoshi Takeo, Sogabe Tomohiro, Miyatake Yuto, Zhang Shao-Liang

JOURNAL OF COMPUTATIONAL PHYSICS 371 巻頁： 618-632 2018年10月

A Look-Back-type restart for the restarted Krylov subspace methods for solving non-Hermitian linear systems 査読有り

Imakura Akira, Sogabe Tomohiro, Zhang Shao-Liang

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 35 巻 ( 2 ) 頁： 835-859 2018年7月

On a relationship between the T-congruence Sylvester equation and the Lyapunov equation 査読有り

Oozawa Masaya, Sogabe Tomohiro, Miyatake Yuto, Zhang Shao-Liang

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 329 巻頁： 51-56 2018年2月

A fast algorithm for solving tridiagonal quasi-Toeplitz linear systems 査読有り

Du Lei, Sogabe Tomohiro, Zhang Shao-Liang

APPLIED MATHEMATICS LETTERS 75 巻頁： 74 - 81 2018年1月

二重指数関数型数値積分公式を用いた行列実数乗の計算査読有り

立岡文理, 曽我部知広, 宮武勇登, Zhang Shao-Liang

日本応用数理学会論文誌(Web) 28 巻 ( 3 ) 頁： 142‐161(J‐STAGE) - 161 2018年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本応用数理学会

概要. 本論文では数値積分による行列実数乗Aαの計算を考える．Aαの積分表示は減衰の遅い被積分関数の広義積分で表される．これまでは，変数変換により積分区間を有限にした後にGauss求積を用いて計算されてきたが，Aの条件数やαによっては収束性が悪化しうる．本論文では新たなアプローチとして二重指数関数型積分公式に着目し，積分区間の設定方法等をまとめたアルゴリズムを示したのち，その有用性を数値的に検証する．

DOI： 10.11540/jsiamt.28.3_142

J-GLOBAL

Solution of a Nonlinear Eigenvalue Problem Using Signed Singular Values 査読有り

Ooi Kouhei, Mizuno Yoshinori, Sogabe Tomohiro, Yamamoto Yusaku, Zhang Shao-Liang

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS 7 巻 ( 4 ) 頁： 799-809 2017年11月

微分方程式に対する離散勾配法に基づく線形方程式の数値解法の生成査読有り

宮武勇登, 曽我部知広, ZHANG Shao-Liang

日本応用数理学会論文誌(Web) 27 巻 ( 3 ) 頁： 239‐249(J‐STAGE) - 249 2017年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本応用数理学会

概要. 本論文では，正定値対称行列を係数行列とする線形方程式に対して，その解を平衡点として持つ常微分方程式の初期値問題に，離散勾配法と呼ばれる常微分方程式の数値解法を適用することで，線形方程式に対する反復法を生成する枠組みを提案する．本枠組みは，無条件収束する反復法を生成でき，また多くの自由度がある中，簡単な例として定常反復法であるSOR 法を包含することを示す．

DOI： 10.11540/jsiamt.27.3_239

J-GLOBAL

On The Pfaflians and Determinants of Some Skew-Centrosymmetric Matrices 査読有り

Fatih Yilmaz, Tomohiro Sogabe, Emrullah Kirklar

JOURNAL OF INTEGER SEQUENCES 20 巻 ( 4 ) 頁： 1 - 9 2017年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：UNIV WATERLOO

This paper shows that the Pfaffians and determinants of some skew centrosymmetric matrices can be computed by a paired two-term recurrence relation, or a general number sequence of second order. As a result, the complexities of the formulas are of order It. Furthermore, the formulas have no divisions at all, i.e., they fall into the class of breakdown-free algorithms.

Web of Science

Scopus

Energy-preserving $H^1$-Galerkin schemes for the Hunter--Saxton equation 査読有り

Yuto Miyatake, Geonsik Eom, Tomohiro Sogabe, Shao-Liang Zhang

Journal of Mathematical Research with Applications 37 巻頁： 107 - 118 2017年

A cost-efficient variant of the incremental Newton iteration for the matrix $p$th root 査読有り

Fuminori Tatsuoka, Tomohiro Sogabe, Yuto Miyatake, Shao-Liang Zhang

Journal of Mathematical Research with Applications ( 37 ) 頁： 97 - 106 2016年11月

An initial guess of Newton's method for the matrix square root based on a sphere constrained optimization problem 査読有り

Mizuno Sho, Moriizumi Yosuke, Usuda Tsuyoshi S., Sogabe Tomohiro

JSIAM Letters 8 巻 ( 0 ) 頁： 17 - 20 2016年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本応用数理学会

In this paper, an initial guess is proposed for Newton's method to compute the principal matrix square root, and a sufficient condition of the initial guess is shown for the quadratic convergence. Numerical examples indicate that the initial guess is promising for computing the principal square roots of overlap matrices arising from condensed matter physics.

DOI： 10.14495/jsiaml.8.17

A generalized symbolic Thomas algorithm for the solution of opposite-bordered tridiagonal linear systems 査読有り

Jiteng Jia, Tomohiro Sogabe, Sumei Li

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 290 巻頁： 423 - 432 2015年12月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：ELSEVIER SCIENCE BV

In the current paper, we present a generalized symbolic Thomas algorithm, that never suffers from breakdown, for solving the opposite-bordered tridiagonal (OBT) linear systems. The algorithm uses a fill-in matrix factorization and can solve an OBT linear system in 0(n) operations. Meanwhile, an efficient method of evaluating the determinant of an opposite-bordered tridiagonal matrix is derived. The computational costs of the proposed algorithms are also discussed. Moreover, three numerical examples are provided in order to demonstrate the performance and effectiveness of our algorithms and their competitiveness with some already existing algorithms. All of the experiments are performed on a computer with the aid of programs written in Matlab. (C) 2015 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.cam.2015.05.026

Web of Science

Scopus

IDR(s) for solving shifted nonsymmetric linear systems 査読有り

Du Lei, Sogabe Tomohiro, Zhang Shao-Liang

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 274 巻頁： 35 - 43 2015年1月

On decomposition of k-tridiagonal l-Toeplitz matrices and its applications 査読有り

Ohashi A., Sogabe T., Usuda T. S.

SPECIAL MATRICES 3 巻 ( 1 ) 頁： 200 - 206 2015年1月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Special Matrices

© 2015 A. Ohashis et al., licensee De Gruyter Open. We consider a k-tridiagonal ℓ-Toeplitz matrix as one of generalizations of a tridiagonal Toeplitz matrix. In the present paper, we provide a decomposition of the matrix under a certain condition. By the decomposition, the matrix is easily analyzed since one only needs to analyze the small matrix obtained from the decomposition. Using the decomposition, eigenpairs and arbitrary integer powers of the matrix are easily shown as applications.

DOI： 10.1515/spma-2015-0019

Web of Science

Scopus

On tensor product decomposition of k-tridiagonal Toeplitz matrices 査読有り

Asuka Ohashi, Tsuyoshi Sasaki Usuda, Tomohiro Sogabe, Fatih Yilmaz

International Journal of Pure and Applied Mathematics 103 巻 ( 3 ) 頁： 537 - 545 2015年

AN EXTENSION OF TWO CONJUGATE DIRECTION METHODS TO MARKOV CHAIN PROBLEMS 査読有り

Chun Wen, Ting-Zhu Huang, Tomohiro Sogabe

COMPUTING AND INFORMATICS 34 巻 ( 2 ) 頁： 495 - 516 2015年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：SLOVAK ACAD SCIENCES INST INFORMATICS

Motivated by the recent applications of the conjugate residual method to nonsymmetric lineal systems by Sogabe, Sugihara and Zhang [An extension of the conjugate residual method to nonsymmetric linear systems. J. Comput. Appl. Math., Vol. 266, 2009, pp. 103-113], this paper describes two conjugate direction methods, BiCR and BiCG, and attempts to extend their applications to compute the stationary probability distribution for an irreducible Markov chain with the aim of finding an alternative basic solver. Numerical experiments show the feasibility of the BiCR and BiCG to some extent, with applications to several practical Markov chain problems.

Web of Science

Quasi-minimal residual variants of the COCG and COCR methods for complex symmetric linear systems in electromagnetic simulations 査読有り

IEEE Trans. Microw. Theory Techn. 62 巻頁： 2859-2867 2014年12月

A note on a fast breakdown-free algorithm for computing the determinants and the permanents of k-tridiagonal matrices 査読有り

Tomohiro Sogabe, Fatih Yilmaz

APPLIED MATHEMATICS AND COMPUTATION 249 巻頁： 98 - 102 2014年12月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：ELSEVIER SCIENCE INC

k-Tridiagonal matrices have attracted much attention in recent years, which are a generalization of tridiagonal matrices. In this note, a breakdown-free numerical algorithm of O(n) is presented for computing the determinants and the permanents of k-tridiagonal matrices. Even though the algorithm is not a symbolic algorithm, it never suffers from breakdown. Furthermore, it produces exact values when all entries of the k-tridiagonal matrices are given in integer. In addition, the algorithm can be simplified for a general symmetric Toeplitz case, and it generates the kth powers of Fibonacci, Pell, and Jacobsthal numbers for a certain symmetric Toeplitz case. (C) 2014 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.amc.2014.10.040

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Scopus

An algorithm for solving nonsymmetric penta-diagonal Toeplitz linear systems 査読有り

Du Lei, Sogabe Tomohiro, Zhang Shao-Liang

APPLIED MATHEMATICS AND COMPUTATION 244 巻頁： 10 - 15 2014年10月

BiCR-type methods for families of shifted linear systems 査読有り

Xian-Ming Gu, Ting-Zhu Huang, Jing Meng, Tomohiro Sogabe, Hou-Biao Li, Liang Li

COMPUTERS & MATHEMATICS WITH APPLICATIONS 68 巻 ( 7 ) 頁： 746 - 758 2014年10月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：PERGAMON-ELSEVIER SCIENCE LTD

The shifted linear systems with non-Hermitian matrices often arise from the numerical solutions for time-dependent PDEs, computing the large-scale eigenvalue problems, control theory and so on. In the present paper, we develop two shifted variants of BiCR-type methods for solving such linear systems. These variants of BiCR-type methods take advantage of the shifted structure, so that the number of matrix-vector multiplications and the number of inner products are the same as a single linear system. Finally, extensive numerical examples are reported to illustrate the performance and effectiveness of the proposed methods. (C) 2014 Elsevier Ltd. All rights reserved.

DOI： 10.1016/j.camwa.2014.07.029

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A note on symmetric k-Tridiagonal matrix family and the Fibonacci numbers 査読有り

Fatih Yilmaz, Tomohiro Sogabe

International Journal of Pure and Applied Mathematics 96 巻 ( 2 ) 頁： 289 - 298 2014年

A novel algorithm for solving quasi penta-diagonal linear systems 査読有り

Ji-Teng Jia, Tomohiro Sogabe

JOURNAL OF MATHEMATICAL CHEMISTRY 51 巻 ( 3 ) 頁： 881 - 889 2013年3月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：SPRINGER

In this paper, a novel numerical algorithm for solving quasi penta-diagonal linear systems is presented. The computational costs of the algorithm is less than those of three successful algorithms given by El-Mikkawy and Rahmo (Comput Math Appl 59:1386-1396, 2010), by Lv and Le (Appl Math Comput 204:707-712, 2008), and by Jia et al. (Int J Comput Math 89:851-860, 2012). In addition, a new recursive method for inverting the quasi penta-diagonal matrices is also discussed. The implementation of the algorithm using Computer Algebra Systems (CASs) such as MATLAB and MAPLE is straightforward. Two numerical examples are given in order to demonstrate the performance and efficiency of our algorithm.

DOI： 10.1007/s10910-012-0122-7

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Scopus

A novel algorithm and its parallelization for solving nearly penta-diagonal linear systems 査読有り

Ji-Teng Jia, Tomohiro Sogabe

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 90 巻 ( 2 ) 頁： 435 - 444 2013年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：TAYLOR & FRANCIS LTD

In the current paper, a new serial algorithm for solving nearly penta-diagonal linear systems is presented. The computational cost of the algorithm is less than or almost equal to those of recent successful algorithms [J. Jia, Q. Kong, and T. Sogabe, A fast numerical algorithm for solving nearly penta-diagonal linear systems, Int. J. Comput. Math. 89 (2012), pp. 851860; X.G. Lv and J. Le, A note on solving nearly penta-diagonal linear systems, Appl. Math. Comput. 204 (2008), pp. 707712; S.N. Neossi Nguetchue and S. Abelman, A computational algorithm for solving nearly penta-diagonal linear systems, Appl. Math. Comput. 203 (2008), pp. 629634]. Moreover, it is suitable for developing its parallel algorithms. One of the parallel algorithms is given and is shown to be promising. The implementation of the algorithms using Computer Algebra Systems such as MATLAB and MAPLE is straightforward. Two numerical examples are given in order to illustrate the validity and efficiency of our algorithms.

DOI： 10.1080/00207160.2012.725845

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Scopus

On particular solution of ordinary differential equations with constant coefficients 査読有り

Jiteng Jia, Tomohiro Sogabe

APPLIED MATHEMATICS AND COMPUTATION 219 巻 ( 12 ) 頁： 6761 - 6767 2013年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：ELSEVIER SCIENCE INC

In this paper, a new method is presented for obtaining the particular solution of ordinary differential equations with constant coefficients. An explicit formula of the particular solution is derived from the use of an upper triangular Toeplitz matrix. The validity of the approach is illustrated by some examples. (C) 2013 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.amc.2012.12.080

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Scopus

Inversion of k-tridiagonal matrices with Toeplitz structure 査読有り

Jiteng Jia, Tomohiro Sogabe, Moawwad El-Mikkawy

COMPUTERS & MATHEMATICS WITH APPLICATIONS 65 巻 ( 1 ) 頁： 116 - 125 2013年1月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：PERGAMON-ELSEVIER SCIENCE LTD

In this paper, we consider an inverse problem with the k-tridiagonal Toeplitz matrices. A theoretical result is obtained that under certain assumptions the explicit inverse of a k-tridiagonal Toeplitz matrix can be derived immediately. Two numerical examples are given to demonstrate the validity of our results. (c) 2012 Elsevier Ltd. All rights reserved.

DOI： 10.1016/j.camwa.2012.11.001

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Scopus

An interior eigenvalue problem from electronic structure calculations 査読有り

Lee Dongjin, Miyata Takafumi, Sogabe Tomohiro, Hoshi Takeo, Zhang Shao-Liang

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 30 巻 ( 3 ) 頁： 625 - 633 2013年

An Efficient Variant of the Restarted Shifted GMRES Method for Solving Shifted Linear Systems 査読有り

Imakura,Akira, Tomohiro,Sogabe, Shao-Liang,Zhang

Journal of Mathematical Research with Applications 33 巻 ( 2 ) 頁： 127 - 141 2013年

記述言語：英語掲載種別：研究論文（学術雑誌）

We investigate the restart of the Restarted Shifted GMRES method for solving shifted linear systems. Recently the variant of the GMRES($m$) method with the {\it unfixed update} has been proposed to improve the convergence of the GMRES($m$) method for solving linear systems, and shown to have an efficient convergence property. In this paper, by applying the unfixed update to the Restarted Shifted GMRES method, we propose a variant of the Restarted Shifted GMRES method. We show a potentiality for efficient convergence within the variant by some numerical results.

Solution of generalized shifted linear systems with complex symmetric matrices 査読有り

Sogabe Tomohiro, Hoshi Takeo, Zhang Shao-Liang, Fujiwara Takeo

JOURNAL OF COMPUTATIONAL PHYSICS 231 巻 ( 17 ) 頁： 5669 - 5684 2012年7月

An order-N electronic structure theory with generalized eigenvalue equations and its application to a ten-million-atom system 査読有り

Hoshi T., Yamamoto S., Fujiwara T., Sogabe T., Zhang S-L

JOURNAL OF PHYSICS-CONDENSED MATTER 24 巻 ( 16 ) 2012年4月

A new algorithm for solving nearly penta-diagonal Toeplitz linear systems 査読有り

Jiteng Jia, Qiongxiang Kong, Tomohiro Sogabe

COMPUTERS & MATHEMATICS WITH APPLICATIONS 63 巻 ( 7 ) 頁： 1238 - 1243 2012年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：PERGAMON-ELSEVIER SCIENCE LTD

A new numerical algorithm for solving nearly penta-diagonal Toeplitz linear systems is presented. The algorithm is suited for implementation using Computer Algebra Systems (CASs) such as MATLAB, MACSYMA and MAPLE. Numerical examples are given in order to illustrate the efficiency of our algorithm. (C) 2011 Elsevier Ltd. All rights reserved.

DOI： 10.1016/j.camwa.2011.12.044

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Scopus

An Efficient Variant of the GMRES(m) Method Based on the Error Equations 査読有り

Imakura Akira, Sogabe Tomohiro, Zhang Shao-Liang

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS 2 巻 ( 1 ) 頁： 19 - 32 2012年2月

デフレーション型とLook-Back型のリスタートを併用したGMRES(m)法の収束特性査読有り

今倉暁, 楊済栄, 曽我部知広, 張紹良

日本応用数理学会論文誌 22 巻 ( 3 ) 頁： 117-141 2012年

記述言語：英語掲載種別：研究論文（学術雑誌）

非対称線形方程式のためのGMRES(m)法に対する改良法として,デフレーション型とLook-Back型のリスタートに着目する.本論文では,残差多項式に基づく解析を通し,両リスタート技法が異なる数理的背景に基づきGMRES(m)法の収束性を改善することを示す.またその事実に基づき,両リスタート技法を併用するGMRES(m)法の改良法を提案し,数値実験からその収束特性を検証する.

DOI： 10.11540/jsiamt.22.3_117

非対称線形方程式のためのLook-Back GMRES(m)法査読有り

今倉暁, 曽我部知広, 張紹良

日本応用数理学会論文誌 22 巻 ( 1 ) 頁： 1-21 2012年

記述言語：英語掲載種別：研究論文（学術雑誌）

近年我々は,非対称線形方程式に対するGMRES(m)法のリスタート時の初期近似解の設定法に着目し,誤差方程式の観点からGMRES(m)法の拡張法を提案した.本論文では,拡張したGMRES(m)法の残差多項式に対する解析を通し,GMRES(m)法の残差多項式を逐次再構築する"Look-Back戦略"に基づくLook-Back GMRES(m)法を提案する.また,Look-Back GMRES(m)法の有効性を数値実験から検証する.

DOI： 10.11540/jsiamt.22.1_1

A fast numerical algorithm for solving nearly penta-diagonal linear systems 査読有り

Ji-teng Jia, Qiong-xiang Kong, Tomohiro Sogabe

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 89 巻 ( 6 ) 頁： 851 - 860 2012年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：TAYLOR & FRANCIS LTD

In this paper, we present a fast numerical algorithm for solving nearly penta-diagonal linear systems and show that the computational cost is less than those of three algorithms in El-Mikkawy and Rahmo, [Symbolic algorithm for inverting cyclic penta-diagonal matrices recursively-Derivation and implementation, Comput. Math. Appl. 59 (2010), pp. 1386-1396], Lv and Le [A note on solving nearly penta-diagonal linear systems, Appl. Math. Comput. 204 (2008), pp. 707-712] and Neossi Nguetchue and Abelman [A computational algorithm for solving nearly penta-diagonal linear systems, Appl. Math. Comput. 203 (2008), pp. 629-634.]. In addition, an efficient way of evaluating the determinant of a nearly penta-diagonal matrix is also discussed. The algorithm is suited for implementation using computer algebra systems (CAS) such as MATLAB, MACSYMA and MAPLE. Some numerical examples are given in order to illustrate the efficiency of our algorithm.

DOI： 10.1080/00207160.2012.665903

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Scopus

Fast block diagonalization of k-tridiagonal matrices 査読有り

Tomohiro Sogabe, Moawwad El-Mikkawy

APPLIED MATHEMATICS AND COMPUTATION 218 巻 ( 6 ) 頁： 2740 - 2743 2011年11月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：ELSEVIER SCIENCE INC

In the present paper, we give a fast algorithm for block diagonalization of k-tridiagonal matrices. The block diagonalization provides us with some useful results: e. g., another derivation of a very recent result on generalized k-Fibonacci numbers in [M. E. A. El-Mikkawy, T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput. 215 (2010) 4456-4461]; efficient (symbolic) algorithm for computing the matrix determinant. (C) 2011 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.amc.2011.08.014

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Scopus

A variant of the IDR(s) method with the quasi-minimal residual strategy 査読有り

Du Lei, Sogabe Tomohiro, Zhang Shao-Liang

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 236 巻 ( 5 ) 頁： 621 - 630 2011年10月

一般化固有値問題に対するArnoldi(M,W,G)法査読有り

山下達也, 宮田考史, 曽我部知広, 星健夫, 藤原毅夫, ZHANG Shao‐Liang

日本応用数理学会論文誌 21 巻 ( 3 ) 頁： 241 - 254 2011年9月

A block IDR(s) method for nonsymmetric linear systems with multiple right-hand sides 査読有り

Du L., Sogabe T., Yu B., Yamamoto Y., Zhang S. -L.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 235 巻 ( 14 ) 頁： 4095 - 4106 2011年5月

Efficient and accurate linear algebraic methods for large-scale electronic structure calculations with nonorthogonal atomic orbitals 査読有り

Teng H., Fujiwara T., Hoshi T., Sogabe T., Zhang S. -L., Yamamoto S.

PHYSICAL REVIEW B 83 巻 ( 16 ) 2011年4月

Quasi-minimal residual smoothing technique for the IDR($s$) method 査読有り

Du Lei, Sogabe Tomohiro, Zhang Shao-Liang

JSIAM Letters 3 巻 ( 0 ) 頁： 13-16 2011年

Four-point correlation function of a passive scalar field in rapidly fluctuating turbulence: Numerical analysis of an exact closure equation 査読有り

Mizuno Y., Ohi K., Sogabe T., Yamamoto Y., Kaneda Y.

PHYSICAL REVIEW E 82 巻 ( 3 ) 2010年9月

Jacobi‐Davidson法における修正方程式の解法―射影空間におけるKrylov部分空間のシフト不変性に基づいて― 査読有り

宮田考史, 曽我部知広, ZHANG Shao‐Liang

日本応用数理学会論文誌 20 巻 ( 2 ) 頁： 115 - 129 2010年6月

Novel algorithm of large-scale simultaneous linear equations 査読有り

Fujiwara T., Hoshi T., Yamamoto S., Sogabe T., Zhang S-L

JOURNAL OF PHYSICS-CONDENSED MATTER 22 巻 ( 7 ) 2010年2月

A new family of k-Fibonacci numbers 査読有り

Moawwad El-Mikkawy, Tomohiro Sogabe

APPLIED MATHEMATICS AND COMPUTATION 215 巻 ( 12 ) 頁： 4456 - 4461 2010年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：ELSEVIER SCIENCE INC

In the present paper, we give a new family of k-Fibonacci numbers and establish some properties of the relation to the ordinary Fibonacci numbers. Furthermore, we describe the recurrence relations and the generating functions of the new family for k = 2 and k = 3, and presents a few identity formulas for the family and the ordinary Fibonacci numbers. (C) 2010 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.amc.2009.12.069

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Notes on particular symmetric polynomials with applications 査読有り

Moawwad El-Mikkawy, Tomohiro Sogabe

APPLIED MATHEMATICS AND COMPUTATION 215 巻 ( 9 ) 頁： 3311 - 3317 2010年1月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：ELSEVIER SCIENCE INC

This paper presents some applications using several properties of three important symmetric polynomials: elementary symmetric polynomials, complete symmetric polynomials and the power sum symmetric polynomials. The applications includes a simple proof of El-Mikkawy conjecture in [M. E. A. El-Mikkawy, Appl. Math. Comput. 146 (2003) 759-769] and a very easy proof of the Newton-Girard formula. In addition, a generalization of Stirling numbers is obtained. (C) 2009 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.amc.2009.10.019

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Scopus

Jacobi-Davidson法における修正方程式の解法 : 射影空間におけるKrylov部分空間のシフト不変性に基づいて(理論)

宮田考史, 曽我部知広, 張紹良

日本応用数理学会論文誌 20 巻 ( 2 ) 頁： 115 - 129 2010年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本応用数理学会

大規模疎行列の一部の固有対を数値的に求めるため,反復法の一種であるJacobi-Davidson(JD)法が近年提案された.JD法は,修正方程式を近似的に解くことにより,部分空間の基底を生成したうえ,固有対の反復解を構築する.このとき,修正方程式の解法によって,JD法の収束性が左右される.本論文ではJD法の収束を速めるため,射影空間におけるKrylov部分空間のシフト不変性を示し,この性質を活用した修正方程式の解法を新たに提案する.

DOI： 10.11540/jsiamt.20.2_115

CiNii Research

GMRES(m)法のリスタートについて査読有り

今倉暁, 曽我部知広, ZHANG Shao‐Liang

日本応用数理学会論文誌 19 巻 ( 4 ) 頁： 551 - 564 2009年12月

多重連結領域の固有値問題に対するSakurai‐Sugiura法の拡張査読有り

宮田考史, DU Lei, 曽我部知広, 山本有作, ZHANG Shao‐Liang

日本応用数理学会論文誌 19 巻 ( 4 ) 頁： 537 - 550 2009年12月

大規模シフト線形方程式の数値解法―クリロフ部分空間の性質に着目して査読有り

曽我部知広, 張紹良

応用数理 19 巻 ( 3 ) 頁： 163 - 178 2009年9月

An extension of the conjugate residual method to nonsymmetric linear systems 査読有り

Sogabe T., Sugihara M., Zhang S. -L.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 226 巻 ( 1 ) 頁： 103 - 113 2009年4月

An implicit wavelet sparse approximate inverse preconditioner using block finger pattern 査読有り

Imakura A., Sogabe T., Zhang S. -L.

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 16 巻 ( 11-12 ) 頁： 915 - 928 2009年

Shifted Conjugate-Orthogonal-Conjugate-Gradient Method and Its Application to Double Orbital Extended Hubbard Model 査読有り

Yamamoto Susumu, Sogabe Tomohiro, Hoshi Takeo, ZHANG Shao-Liang, FUJIWARA Takeo

Journal of the Physical Society of Japan 77 巻 ( 11 ) 頁： "114713-1"-"114713-8" 2008年11月

New algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems 査読有り

Sogabe Tomohiro

APPLIED MATHEMATICS AND COMPUTATION 202 巻 ( 2 ) 頁： 850 - 856 2008年8月

A note on "A fast numerical algorithm for the determinant of a pentadiagonal matrix" 査読有り

Sogabe Tomohiro

APPLIED MATHEMATICS AND COMPUTATION 201 巻 ( 1-2 ) 頁： 561 - 564 2008年7月

Numerical algorithms for solving comrade linear systems based on tridiagonal solvers 査読有り

Sogabe Tomohiro

APPLIED MATHEMATICS AND COMPUTATION 198 巻 ( 1 ) 頁： 117 - 122 2008年4月

A fast numerical algorithm for the determinant of a pentadiagonal matrix 査読有り

Sogabe Tomohiro

APPLIED MATHEMATICS AND COMPUTATION 196 巻 ( 2 ) 頁： 835 - 841 2008年3月

AOR法を用いた可変的前処理付き一般化共役残差法査読有り

前田祥兵, 阿部邦美, 曽我部知広, 張紹良

日本応用数理学会論文誌 18 巻 ( 1 ) 頁： 155-170 2008年

ON A WEIGHTED QUASI-RESIDUAL MINIMIZATION STRATEGY FOR SOLVING COMPLEX SYMMETRIC SHIFTED LINEAR SYSTEMS 査読有り

T. Sogabe, T. Hoshi, S. -L. Zhang, T. Fujiwara

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 31 巻頁： 126 - 140 2008年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：KENT STATE UNIVERSITY

We consider the solution of complex symmetric shifted linear systems. Such systems arise in large-scale electronic structure simulations, and there is a strong need of algorithms for their fast solution. With the aim of solving the systems efficiently, we consider a special case of the QMR method for non-Hermitian shifted linear systems and propose its weighted quasi-minimal residual approach. A numerical algorithm, referred to as shifted QMR_SYM(B), is obtained by the choice of a weight which is particularly cost-effective. Numerical examples are presented to show the performance of the shifted QMR_SYM(B) method.

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Finger patternのブロック化による陰的wavelet近似逆行列前処理の高速化査読有り

今倉暁, 曽我部知広, ZHANG Shao‐Liang

日本応用数理学会論文誌 17 巻 ( 4 ) 頁： 523 - 542 2007年12月

Bi‐CR法への準最小残差アプローチの適用について査読有り

南さつき, 曽我部知広, 杉原正顯, ZHANG Shao‐Liang

日本応用数理学会論文誌 17 巻 ( 3 ) 頁： 301 - 317 2007年9月

非対称行列用共役残差法に基づく積型反復解法査読有り

阿部邦美, 曽我部知広, 藤野清次, 張紹良

情報処理学会論文誌コンピューティングシステム（ACS） 48 巻 ( 8 ) 頁： 11-21 2007年5月

記述言語：英語掲載種別：研究論文（学術雑誌）

我々は非対称行列用共役残差法の残差多項式の係数の計算方法を積型反復解法に取り入れることによって新たな積型反復解法を提案する．すなわち，残差，近似解を生成するための漸化式は従来の積型反復解法と同一のものを用い，従来の双共役勾配法の残差多項式の係数の代わりに非対称行列用共役残差法の残差多項式の係数を用いてアルゴリズムを更新する．数値実験では，非対称行列用CR法に基づく積型反復解法が従来の積型反復解法よりも有効であることを示す．We propose a product-type Krylov subspace method based on the conjugate residual (CR) method for nonsymmetric coefficient matrices. The recurrence formulas for updating an approximation and a residual vector are the same as those of the original product-type Krylov subspace method, while the recurrence coefficients alpha_k and beta_k are determined so as to compute the coefficients of the residual polynomial of CR for nonsymmetric coefficient matrices. Numerical experiments show that our proposed product-type Krylov subspace method is more effective than the original.

On a two-term recurrence for the determinant of a general matrix 査読有り

T. Sogabe

Appl. Math. Comput. 187 巻頁： 785-788 2007年

A COCR method for solving complex symmetric linear systems 査読有り

T. Sogabe and S.-L. Zhang

J. Comput. Appl. Math. 199 巻頁： 297-303 2007年

A numerical method for calculating the green's function arising from electronic structure theory 査読有り

Tomohiro Sogabe, Takeo Hoshi, Shao-Liang Zhang, Takeo Fujiwara

FRONTIERS OF COMPUTATIONAL SCIENCE 頁： 189 - + 2007年

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：SPRINGER-VERLAG BERLIN

We developed a fast numerical method for complex symmetric shifted linear systems, which is motivated by the quantum-mechanical (electronic-structure) theory in nanoscale materials. The method is named shifted Conjugate Orthogonal Conjugate Gradient (shifted COCG) method. The formulation is given and several numerical aspects are discussed.

DOI： 10.1007/978-3-540-46375-7_24

Web of Science

Linear algebraic calculation of Green's function for large-scale electronic structure theory 査読有り

R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, and T. Fujiwara

Phys. Rev. B 165108 巻頁： 1-9 2006年

非対称Toeplitz行列のための置換行列による前処理査読有り

曽我部知広, ZHENG Bo, 橋本康, ZHANG Shao‐Liang

日本応用数理学会論文誌 15 巻 ( 2 ) 頁： 159 - 168 2005年6月

共役残差法の非対称行列用への拡張査読有り

曽我部知広，杉原正顯，張紹良

日本応用数理学会論文誌 15 巻 ( 3 ) 頁： 445-459 2005年

CGS法の改良について査読有り

曽我部知広，金成海，阿部邦美，張紹良

日本応用数理学会論文誌 14 巻 ( 1 ) 頁： 1-12 2004年

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