研究者詳細 - 曽我部　知広

論文 - 曽我部　知広

分割表示 95 件中 1 - 20 件目／全件表示 >>

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 <i>M</i>-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