Faculty Profiles - SOGABE, Tomohiro

Papers - SOGABE, Tomohiro

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Relation between the T-congruence Sylvester equation and the generalized Sylvester equation Reviewed

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

APPLIED MATHEMATICS LETTERS Vol. 96 page： 7 - 13 2019.10

Language：English Publishing type：Research paper (scientific journal) Publisher：PERGAMON-ELSEVIER SCIENCE LTD

The T-congruence Sylvester equation is the matrix equation AX + (XB)-B-T = C, where A is an element of R-mxn, B is an element of R-nxm, and C is an element of R-mxm are given, and X is an element of R-nxm is to be determined. Recently, Oozawa et al. discovered a transformation that the matrix equation is equivalent to one of the well-studied matrix equations (the Lyapunov equation); however, the condition of the transformation seems to be too limited because matrices A and B are assumed to be square matrices (m = n). In this paper, two transformations are provided for rectangular matrices A and B. One of them is an extension of the result of Oozawa et al. for the case m >= n, and the other is a novel transformation for the case m <= n. (C) 2019 Elsevier Ltd. All rights reserved.

DOI： 10.1016/j.aml.2019.04.007

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Bidiagonalization of (k, k + 1)-tridiagonal matrices Reviewed

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

SPECIAL MATRICES Vol. 7 ( 1 ) page： 20-26 2019.1

On computing the minimum singular value of a tensor sum Reviewed

A. Ohashi, T. Sogabe

Special Matrices Vol. 7 ( 1 ) page： 95 - 106 2019.1

Language：English Publishing type：Research paper (scientific journal)

© 2019 A. Ohashi et al., published by De Gruyter. Recently, the Lanczos bidiagonalization method over tensor space has been proposed for computing the maximum and minimum singular values of a tensor sum T. The method over tensor space is practical in memory and has a simple implementation due to recent developments in tensor computations; however, there is still room for improvement in the convergence to the minimum singular value. This study reconstructed an invert Lanczos bidiagonalization method from vector space to tensor space. The resulting algorithm requires solving linear systems at each iteration step. Using standard direct methods, such as the LU decomposition for solving the linear systems requires a huge memory of O(n6). Therefore, this paper proposes a tensor-structure-preserving direct methods of T whose memory requirements are of O(n3), which is equivalent to the order of iterative methods. Numerical examples indicate that the number of iterations tends to be much smaller than that of the conventional method.

DOI： 10.1515/spma-2019-0009

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

Yuto Miyatake, Tai Nakagawa, Tomohiro Sogabe, Shao Liang Zhang

Journal of Computational Dynamics Vol. 6 ( 2 ) page： 361 - 383 2019

Language：English Publishing type：Research paper (scientific journal)

©2019 American Institute of Mathematical Sciences. We propose a Fourier pseudo-spectral scheme for the space-fractional nonlinear Schrödinger equation. The proposedscheme has the following features:it is linearly implicit, it preserves two invariants of the equation, its unique solvability is guaranteed without any restrictions on space and time step sizes. The scheme requires solving a complex symmetric linear system per time step. To solve the system efficiently, we also present a certain variable transformation and preconditioner.

DOI： 10.3934/jcd.2019018

Scopus

On Computing the k-th Singular Triplet Reviewed

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) Vol. 29 ( 1 ) page： 121‐140(J‐STAGE) - 140 2019

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：The Japan Society for Industrial and Applied Mathematics

Abstract. We propose a numerical algorithm for the problem of computing the k-th singular triplet of a large sparse matrix. In the proposed algorithm, the problem is divided into subproblems, and then eigenvalue problems equivalent to the singular value problem are solved in each subproblem. We discuss the accuracy of the proposed algorithm and show that it can handle large matrices in numerical experiments.

DOI： 10.11540/jsiamt.29.1_121

J-GLOBAL

Modified Strang splitting for semilinear parabolic problems Reviewed

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

JSIAM LETTERS Vol. 11 ( 0 ) page： 77 - 80 2019

Language：English Publishing type：Research paper (scientific journal) Publisher：JAPAN SOC INDUSTRIAL & APPLIED MATHEMATICS-JSIAM

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

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On the equivalence between SOR-type methods for linear systems and the discrete gradient methods for gradient systems Reviewed

Miyatake Yuto, Sogabe Tomohiro, Zhang Shao-Liang

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Vol. 342 page： 58-69 2018.11

Solution of the k-th eigenvalue problem in large-scale electronic structure calculations Reviewed

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

JOURNAL OF COMPUTATIONAL PHYSICS Vol. 371 page： 618-632 2018.10

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

Imakura Akira, Sogabe Tomohiro, Zhang Shao-Liang

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS Vol. 35 ( 2 ) page： 835-859 2018.7

On a relationship between the T-congruence Sylvester equation and the Lyapunov equation Reviewed

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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Vol. 329 page： 51-56 2018.2

A fast algorithm for solving tridiagonal quasi-Toeplitz linear systems Reviewed

Lei Du, Tomohiro Sogabe, Shao-Liang Zhang

APPLIED MATHEMATICS LETTERS Vol. 75 page： 74 - 81 2018.1

Language：English Publishing type：Research paper (scientific journal) Publisher：PERGAMON-ELSEVIER SCIENCE LTD

In this paper, we consider the solution of tridiagonal quasi-Toeplitz linear systems. By exploiting the special quasi-Toeplitz structure, we give a new decomposition form of the coefficient matrix. Based on this matrix decomposition form and combined with the Sherman Morrison formula, we propose an efficient algorithm for solving the tridiagonal quasi-Toeplitz linear systems. Although our algorithm takes more floating-point operations (FLOPS) than the LU decomposition method, it needs less memory storage and data transmission and is about twice faster than the LU decomposition method. Numerical examples are given to illustrate the efficiency of our algorithm. (C) 2017 Elsevier Ltd. All rights reserved.

DOI： 10.1016/j.aml.2017.06.016

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A Note on Computing the Matrix Fractional Power Using the Double Exponential Formula Reviewed

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) Vol. 28 ( 3 ) page： 142‐161(J‐STAGE) - 161 2018

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：The Japan Society for Industrial and Applied Mathematics

Abstract. The matrix fractional power Aα can be represented as an improper integral for a slowly decaying function over the half infinite interval. Conventional approaches to approximating the integral are to apply Gaussian quadrature after some variable transformations; however, the convergence could be slow for an ill-conditioned matrix or a specific value of α. To avoid such situation, we consider the Double Exponential (DE) formula instead of conventional approaches, propose algorithms with settings of the integration interval, and then we show some numerical results.

DOI： 10.11540/jsiamt.28.3_142

J-GLOBAL

Solution of a Nonlinear Eigenvalue Problem Using Signed Singular Values Reviewed

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

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS Vol. 7 ( 4 ) page： 799-809 2017.11

The Discrete Gradient Method for Differential Equations Can Be a Generator of Linear Solvers Reviewed

宮武勇登, 曽我部知広, ZHANG Shao-Liang

日本応用数理学会論文誌(Web) Vol. 27 ( 3 ) page： 239‐249(J‐STAGE) - 249 2017

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：The Japan Society for Industrial and Applied Mathematics

Abstract. A novel framework of generating iterative solvers for symmetric positive definite linear systems is proposed. In the framework, iterative solvers are generated by applying the discrete gradient method to initial value problems whose equilibrium coincides with the exact solution of the linear systems. The framework can generate potentially a large number of linear solvers with unconditional convergence property. As a simple example, we show that the framework includes the SOR method.

DOI： 10.11540/jsiamt.27.3_239

J-GLOBAL

On The Pfaflians and Determinants of Some Skew-Centrosymmetric Matrices Reviewed

Fatih Yilmaz, Tomohiro Sogabe, Emrullah Kirklar

JOURNAL OF INTEGER SEQUENCES Vol. 20 ( 4 ) page： 1 - 9 2017

Language：English Publishing type：Research paper (scientific journal) Publisher：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.

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Energy-preserving $H^1$-Galerkin schemes for the Hunter--Saxton equation Reviewed

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

Journal of Mathematical Research with Applications Vol. 37 page： 107 - 118 2017

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

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

Journal of Mathematical Research with Applications ( 37 ) page： 97 - 106 2016.11

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

Sho Mizuno, Yosuke Moriizumi, Tsuyoshi Sasaki Usuda, Tomohiro Sogabe

JSIAM Lett. Vol. 8 ( 0 ) page： 17 - 20 2016

A generalized symbolic Thomas algorithm for the solution of opposite-bordered tridiagonal linear systems Reviewed

Jiteng Jia, Tomohiro Sogabe, Sumei Li

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Vol. 290 page： 423 - 432 2015.12

Language：English Publishing type：Research paper (scientific journal) Publisher：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

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IDR(s) for solving shifted nonsymmetric linear systems Reviewed

Lei Du, Tomohiro Sogabe, Shao-Liang Zhang

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Vol. 274 page： 35 - 43 2015.1

Language：English Publishing type：Research paper (scientific journal) Publisher：ELSEVIER

The IDR(s) method by Sonneveld and van Gijzen (2008) has recently received tremendous attention since it is effective for solving nonsymmetric linear systems. In this paper, we generalize this method to solve shifted nonsymmetric linear systems. When solving this kind of problem by existing shifted Krylov subspace methods, we know one just needs to generate one basis of the Krylov subspaces due to the shift-invariance property of Krylov subspaces. Thus the computation cost required by the basis generation of all shifted linear systems, in terms of matrix vector products, can be reduced. For the IDR(s) method, we find that there also exists a shift-invariance property of the Sonneveld subspaces. This inspires us to develop a shifted version of the IDR(s) method for solving the shifted linear systems. (C) 2014 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.cam.2014.07.004

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Papers - SOGABE, Tomohiro