Transactions of the Japan Society for Industrial and Applied Mathematics

[title in Japanese]

Article type: Cover
2013 Volume 23 Issue 2 Pages Cover1-
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_Cover1

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[title in Japanese]

Article type: Cover
2013 Volume 23 Issue 2 Pages Cover2-
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_Cover2

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[title in Japanese]

Article type: Appendix
2013 Volume 23 Issue 2 Pages App1-
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_App1

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[title in Japanese]

[in Japanese]

Article type: Article
2013 Volume 23 Issue 2 Pages i-
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_i

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Discrete Legendre Duality in Polynomial Matrices(Theory)

Satoshi Moriyama, Kazuo Murota

Article type: Article
2013 Volume 23 Issue 2 Pages 183-202
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_183

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This paper shows the discrete Legendre duality between the two linear algebraic characteristics of polynomial matrices, degrees of subdeterminants and ranks of expanded matrices. The duality also holds between their combinatorial counterparts in graph theory, which serve as upper bounds on the corresponding linear algebraic quantities. Tightness of one of the combinatorial bounds is shown to be equivalent to that of the other. These results extend the recent results for matrix pencils obtained by Murota, and have applications to combinatorial analysis of the Smith-McMillan form at infinity of a rational function matrix.

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Discrete Variational Derivative Method Based on the Compact Finite Differences(Theory)

Hiroki Kanazawa, Takayasu Matsuo, Takaharu Yaguchi

Article type: Article
2013 Volume 23 Issue 2 Pages 203-232
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_203

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For partial differential equations having conserved quantities, such as soliton equations, the "structure-preserving methods" which preserve the invariants are advantageous. On the other hand, in the field of computational fluid dynamics, a special difference method, called "compact difference method," has been widely used due to its high efficiency in wave propagation problems. In this paper, it is shown that the two methods can be combined, i.e., the compact difference method can be incorporated into a structure-preserving method, "the discrete variational derivative method," to construct efficient conservative finite difference schemes. Several numerical experiments are also included.

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Discrete Convex Optimization Solvers and Demonstration Softwares

Nobuyuki Tsuchimura, Satoko Moriguchi, Kazuo Murota

Article type: Article
2013 Volume 23 Issue 2 Pages 233-252
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_233

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In the last decade, efficient discrete optimization algorithms have been proposed in discrete convex analysis, which is a unified framework of discrete convex optimization based on the theory of matroids and submodular functions. With a view to disseminating these theoretical results in application fields, we have developed softwares and web applications of fundamental algorithms for discrete convex minimization.

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Preconditioned Algorithm of the CGS Method Focusing on Its Deriving Process

Shoji Itoh, Masaaki Sugihara

Article type: Article
2013 Volume 23 Issue 2 Pages 253-286
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_253

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In this paper, improved preconditioned algorithms of the CGS method (improved PCGS) are proposed. These improved PCGS algorithms retain some mathematical properties that are accompanied with the CGS derivation from the BiCG method. Rationalities of these improved algorithms are discussed and numerical results illustrate the availability of them. Further, mathematical structure between the conventional PCGS and the improved PCGS is analyzed from the viewpoint of the Krylov subspace. This improvement can be applied to preconditioned algorithms involving the initial shadow residual vector, not only to the PCGS.

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Numerical Experiment of Ship Roll Motion by using Self-Generating Radial Basis Functions Network

Kimihiko Ueno, Chunming Fan

Article type: Article
2013 Volume 23 Issue 2 Pages 287-306
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_287

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It is extremely difficult to estimate the parameters for the equation of ship roll motion, as compared to the other six degrees of freedom ship motion. Previously, Haddara et al. presented a method for estimating the non-linear term in the equation of motion by using a conventional neural network. In this study, numerical experiments were performed by estimating the non-linear term in the equation of ship roll motion by using the Self-Generating Radial Basis Function network developed by Katayama et al.

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Estimation of Parameters in Forced Mathieu Equation with Damping Term

Masaki Yazawa, Kimihiko Ueno, Chunming Fan

Article type: Article
2013 Volume 23 Issue 2 Pages 307-324
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_307

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In this study, we propose a method for estimating parameters of the forced Mathieu equation with a damping term. This method is based on a genetic algorithm(GA). The estimation method using GA was proposed by Ueno et al. The proposed method extended a range of applications from constant parameters to time-varying parameters. Although accurate and efficient estimation of the Mathieu equation from a measured value is difficult, the proposed method enables it. The proposed method is applicable not only to the Mathieu equation but also to other equations of motion with time-varying parameters.

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A Way of Overcoming the Negative-Sign Problem in Ultradiscretization(Survey,<Special Topics>Activity Group "AppIied Integrable Systems")

Shin Isojima, Junkichi Satsuma

Article type: Article
2013 Volume 23 Issue 2 Pages 325-339
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_325

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Ultradiscretization is a limiting procedure transforming a given difference equation into a cellular automaton. To apply this procedure, however, the difference equation and its solution must be subtraction-free and positive-definite, respectively. This restriction is called 'negative-sign problem in ultradiscretization'. In this article, a review of recent research on ultradiscretization with parity variables, which resolves the problem, is given.

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From Orthogonal Polynomials to Integrable Systems(Survey,<Special Topics>Activity Group "AppIied Integrable Systems")

Kazuki Maeda, Hiroshi Miki, Satoshi Tsujimoto

Article type: Article
2013 Volume 23 Issue 2 Pages 341-380
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_341

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Orthogonal polynomials are known to have a close relationship to a lot of areas including integrable systems. We introduce the orthogonal polynomials and its generalizations and review the related integrable systems. We also review how such polynomials are related to recent topics.

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[title in Japanese]

Article type: Appendix
2013 Volume 23 Issue 2 Pages App2-
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_App2

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[title in Japanese]

Article type: Appendix
2013 Volume 23 Issue 2 Pages App3-
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_App3

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[title in Japanese]

Article type: Cover
2013 Volume 23 Issue 2 Pages Cover3-
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_Cover3

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[title in Japanese]

Article type: Cover
2013 Volume 23 Issue 2 Pages Cover4-
Published: June 25, 2013
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.23.2_Cover4

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