Transactions of the Japan Society for Industrial and Applied Mathematics

[title in Japanese]

Article type: Cover
2005 Volume 15 Issue 2 Pages Cover1-
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_Cover1

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[title in Japanese]

Article type: Cover
2005 Volume 15 Issue 2 Pages Cover2-
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_Cover2

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[title in Japanese]

Article type: Appendix
2005 Volume 15 Issue 2 Pages App1-
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_App1

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[title in Japanese]

[in Japanese]

Article type: Article
2005 Volume 15 Issue 2 Pages i-
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_i

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A direct criterion of H-matrix

Hiroshi Niki, Kensaku Tomura, Masataka Usui, Lei Li, Masaaki Sugihara

Article type: Article
2005 Volume 15 Issue 2 Pages 45-58
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_45

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Some iterative criteria for H-matrix are proposed [5][7][8][10]. These methods are judged by generating H or non H-matrices. Therefore, the main drawback of these methods is that when A is an H-matrix, several number of iterations is necessary. To overcome this drawback, in the paper we propose a new semi-direct criterion for H-matrix. Numerical examples are also given.

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A Closed-form Solution of Weather Derivative as an Example of Indifference Prices Under Exponential Preferences

Koichi Miyazaki

Article type: Article
2005 Volume 15 Issue 2 Pages 59-72
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_59

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In this research, I derive a closed-form solution of weather derivative as an example of indifference prices under exponential preferences and then examine the price sensitivities of the derivative. To the goal, firstly, I point out the continuous form of Dischel model is Hull and While model in the literature of interest rate model. Secondly, I derive the process of the accumulated temperature process based on the continuous Dischel model.

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Computing RUR Solutions to Systems of Algebraic Equations by Matrix Eigenproblems

Shuichi Moritsugu

Article type: Article
2005 Volume 15 Issue 2 Pages 73-87
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_73

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We show another formulation for computing RUR (Rational Univariate Representation) solutions to systems of algebraic equations. This algorithm is based on the symbolic computation of the eigenproblem method to polynomial systems. The clue to a practical implementation is the speedup of Frobenius normal forms computation by modular methods. The result of computational experiment is shown and the practicality of the algorithms is discussed.

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An Extension of Divide-and-Conquer for Real Symmetric Tridiagonal Eigenproblem(<Special Issue>Algorithms for Matrix・Eigenvalue Problems and their Applications)

Yutaka Kuwajima, Takaomi Shigehara

Article type: Article
2005 Volume 15 Issue 2 Pages 89-115
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_89

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Divide-and-conquer (DC) is one of the fastest algorithms for eigenproblem of a large-size symmetric tridiagonal matrix (STM). In the original DC, a STM is supposed to be divided in half. In this paper, we propose an extended DC (EDC) where a STM is divided into k parts (k>2). Compared to DC, EDC requires only 3k/(2(k^2-1)) floating operation counts if k is much smaller than the matrix size. In implementation of EDC, the orthogonality among eigenvectors with nearly multiple eigenvalues is ensured by an appropriate usage of quadruple-precision floating-point number processing. We give a formula for the floating operation counts of the present implementation, whose validity is confirmed by numerical experiment.

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High Performance Implementation of Matrix-vector Multiplications in Large-scale Sparse Matrix Eigenvalue Computations on the SMP-type Parallel Computer(<Special Issue>Algorithms for Matrix・Eigenvalue Problems and their Applications)

Mitsuyoshi Igai, Ken Naono, Hiroyuki Kidachi

Article type: Article
2005 Volume 15 Issue 2 Pages 117-128
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_117

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Large-scale sparse matrix computations perform unsatisfactory on the parallel computers. The aim of this paper is to present a high performance implementation of Lanczos eigensolver. A method of bandwidth reduction type ordering is applied for matrix-vector multiplications, one of the main parts in Lanczos eigensolvers. The results show that the implementation with the method performs about 1.6 times faster in the best case. This implies that the ordering, which is known as effective in linear solvers, is also effective in the eigensolver.

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A stabilization of the CGS method by restarting Lanczos process(<Special Issue>Algorithms for Matrix・Eigenvalue Problems and their Applications)

Hiroto TADANO, Tetsuya SAKURAI

Article type: Article
2005 Volume 15 Issue 2 Pages 129-143
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_129

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The Conjugate Gradient Squared (CGS) method has been proposed for solving linear systems with non-Hermitian matrix. This method is known to be unstable because the residual often increases rapidly due to near-breakdown. In this paper, we analyze two causes of near-breakdown in the CGS method and derive a condition of detecting it. Moreover, we propose a method for avoiding near-breakdown in the CGS method by restarting Lanczos process. Effects of the CGS method with restart have been illustrated by some numerical experiments.

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Finite Element Parallel Eigenvalue Analysis Based on Arnoldi Method Using Krylov Subspace Iterative Method(<Special Issue>Algorithms for Matrix・Eigenvalue Problems and their Applications)

Junichi Matsumoto

Article type: Article
2005 Volume 15 Issue 2 Pages 145-158
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_145

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Arnoldi method using Krylov subspace iterative method with spectrum transformation is proposed for the finite element parallel eigenvalue analysis. The finite element eigenvalue analysis using element by element method is investigated numerical accuracy and efficiency of the calculation time and memory. As for the presented method, a three dimensional analysis of Helmholtz problem over one hundred million degree of freedom is realized by a middle-size PC cluster with 64 CPUs. Structure eigenvalue analysis of real model over one hundred million degree of freedom is calculated in this paper.

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A Preconditioner of Permutation Matrix for Solving Nonsymmetric Toeplitz Linear Systems(<Special Issue>Algorithms for Matrix・Eigenvalue Problems and their Applications)

Tomohiro SOGABE, Bo ZHENG, Koh HASHIMOTO, Shao Liang ZHANG

Article type: Article
2005 Volume 15 Issue 2 Pages 159-168
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_159

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We consider the solution of nonsymmetric Toeplitz linear systems using Krylov Subspace (KS) methods. In this paper, a preconditioner of permutation matrix is proposed for improving the performance of the KS methods. Numerical experiments show that this preconditioner gives attractive convergence behavior of the KS methods.

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Large-Scale Molecular Orbital Calculation using FMO-MO Method : characters of eigenvalue problem to be solved in FMO-MO method(<Special Issue>Algorithms for Matrix・Eigenvalue Problems and their Applications)

Yuichi Inadomi, Hiroaki Umeda, Toshio Watanabe, Tetsuya Sakurai, Umpei ...

Article type: Article
2005 Volume 15 Issue 2 Pages 169-179
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_169

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Characters of generalized eigenvalue problem in FMO-MO method, which is one of the fastest methods to calculate molecular orbitals of large molecules such as proteins, are described in order to solve it efficiently. Fock matrix to solve looks dense, because 7.6% of elements have significant value even for a large molecule. The frontier orbital energies can be estimated from fragment and fragment-pair orbital energy distributions in FMO method, which is performed in FMO-MO calculation, and then the frontier orbitals can be obtained efficiently by the method to solve eigenvalue problem in a specific energy region.

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Recent Developments in Algorithms for Solving Dense Eigenproblems (I) : Algorithm of Multiple Relatively Robust Representations(<Special Issue>Algorithms for Matrix・Eigenvalue Problems and their Applications)

Yusaku Yamamoto

Article type: Article
2005 Volume 15 Issue 2 Pages 181-208
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_181

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The Algorithm of Multiple Relatively Robust Representations (MR^3) is a new algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem proposed by I. Dhillon in 1997. It has attracted much attention because it can compute all the eigenvectors of an n×n matrix in only O(n^2) work and is easy to parallelize. In this article, we survey the papers related to the MR^3 algorithm and try to present a simple and easily understandable picture of the algorithm by explaining, one by one, its key ingredients such as the relatively robust representations of a symmetric tridiagonal matrix, the dqds algorithm for computing accurate eigenvalues and the twisted factorization for computing accurate eigenvectors. Limitations of the algorithm and directions for future research are also discussed.

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[title in Japanese]

Article type: Appendix
2005 Volume 15 Issue 2 Pages App2-
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_App2

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[title in Japanese]

Article type: Appendix
2005 Volume 15 Issue 2 Pages App3-
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_App3

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[title in Japanese]

Article type: Appendix
2005 Volume 15 Issue 2 Pages App4-
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_App4

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[title in Japanese]

Article type: Cover
2005 Volume 15 Issue 2 Pages Cover3-
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_Cover3

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[title in Japanese]

Article type: Cover
2005 Volume 15 Issue 2 Pages Cover4-
Published: June 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.2_Cover4

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