Faculty Profiles - SOGABE, Tomohiro

Papers - SOGABE, Tomohiro

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A note on "A fast numerical algorithm for the determinant of a pentadiagonal matrix" Reviewed

Tomohiro Sogabe

APPLIED MATHEMATICS AND COMPUTATION Vol. 201 ( 1-2 ) page： 561 - 564 2008.7

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

A fast numerical algorithm for evaluating the determinant of a pentadiagonal matrix has been recently proposed [T. Sogabe, A fast numerical algorithm for the determinant of a pentadiagonal matrix, Appl. Math. Comput. 196 (2008) 835-841]. The algorithm whose cost is 14n - 28, where n(>= 3) denotes the size of the matrix, is composed of two steps: first, transform a pentadiagonal matrix into sparse Hessenberg form; second, run a numerical algorithm for computing the determinant of the sparse Hessenberg matrix. In this note, it is shown that we have an algorithm with the cost of 13n - 24 by applying twice the idea of the sparse Hessenberg transformation to a pentadiagonal matrix. (c) 2008 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.amc.2007.12.047

Web of Science

Scopus

Numerical algorithms for solving comrade linear systems based on tridiagonal solvers Reviewed

Tomohiro Sogabe

APPLIED MATHEMATICS AND COMPUTATION Vol. 198 ( 1 ) page： 117 - 122 2008.4

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

Recently, two efficient algorithms for solving comrade linear systems have been proposed by Karawia [A. A. Karawia, Two algorithms for solving comrade linear systems, Appl. Math. Comput. 189 (2007) 291-297]. The two algorithms are based on the LU decomposition of the comrade matrix. In this paper, two algorithms are presented for solving the comrade linear systems based on the use of conventional fast tridiagonal solvers and an efficient way of evaluating the determinant of the comrade matrix is discussed. (C) 2007 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.amc.2007.08.029

Web of Science

Scopus

A fast numerical algorithm for the determinant of a pentadiagonal matrix Reviewed

Tomohiro Sogabe

APPLIED MATHEMATICS AND COMPUTATION Vol. 196 ( 2 ) page： 835 - 841 2008.3

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

Recently, a two-term recurrence for the determinant of a general matrix has been found [T. Sogabe, On a two-term recurrence for the determinant of a general matrix, Appl. Math. Comput., 187 (2007) 785-788] and it leads to a natural generalization of the DETGTRI algorithm [M. El-Mikkawy, A fast algorithm for evaluating nth order tridiagonal determinants, J. Comput. Appl. Math. 166 (2004) 581-584] for computing the determinant of a tridiagonal matrix. In this paper, we derive a fast numerical algorithm for computing the determinant of a pentadiagonal matrix from the generalization of the DETGTRI algorithm. (C) 2007 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.amc.2007.07.015

Web of Science

Scopus

AOR法を用いた可変的前処理付き一般化共役残差法 Reviewed

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 Vol. 18 ( 1 ) page： 155-170 2008

ON A WEIGHTED QUASI-RESIDUAL MINIMIZATION STRATEGY FOR SOLVING COMPLEX SYMMETRIC SHIFTED LINEAR SYSTEMS Reviewed

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

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS Vol. 31 page： 126 - 140 2008

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

Web of Science

Scopus

An Efficient Implicit Wavelet Sparse Approximate Inverse Preconditioner Using Blocked Finger Pattern Reviewed

今倉暁, 曽我部知広, ZHANG Shao‐Liang

日本応用数理学会論文誌 Vol. 17 ( 4 ) page： 523 - 542 2007.12

On an application of the QMR approach to the Bi‐CR method Reviewed

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 Vol. 17 ( 3 ) page： 301 - 317 2007.9

A Product-type Krylov Subspace Method Based on Conjugate Residual Method for Nonsymmetric Coefficient Matrices Reviewed

ABE KUNIYOSHI, SOGABE TOMOHIRO, FUJINO SEIJI, ZHANG SHAO-LIANG

Vol. 48 ( 8 ) page： 11-21 2007.5

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

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 α_κ and β_κ 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 Reviewed

T. Sogabe

Appl. Math. Comput. Vol. 187 page： 785-788 2007

A COCR method for solving complex symmetric linear systems Reviewed

T. Sogabe and S.-L. Zhang

Vol. 199 page： 297-303 2007

A numerical method for calculating the green's function arising from electronic structure theory Reviewed

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

FRONTIERS OF COMPUTATIONAL SCIENCE page： 189 - + 2007

Language：English Publishing type：Research paper (international conference proceedings) Publisher：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 Reviewed

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

Phys. Rev. B Vol. 165108 page： 1-9 2006

A Preconditioner of Permutation Matrix for Solving Nonsymmetric Toeplitz Linear Systems Reviewed

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

日本応用数理学会論文誌 Vol. 15 ( 2 ) page： 159 - 168 2005.6

共役残差法の非対称行列用への拡張 Reviewed

曽我部知広，杉原正顯，張紹良

日本応用数理学会論文誌 Vol. 15 ( 3 ) page： 445-459 2005

CGS法の改良について Reviewed

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 Vol. 14 ( 1 ) page： 1-12 2004

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Papers - SOGABE, Tomohiro