Transactions of the Japan Society for Industrial and Applied Mathematics

[title in Japanese]

Article type: Cover
2012 Volume 22 Issue 3 Pages Cover1-
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_Cover1

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[title in Japanese]

Article type: Cover
2012 Volume 22 Issue 3 Pages Cover2-
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_Cover2

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[title in Japanese]

Article type: Appendix
2012 Volume 22 Issue 3 Pages App1-
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_App1

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[title in Japanese]

[in Japanese]

Article type: Article
2012 Volume 22 Issue 3 Pages i-
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_i

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Apportionment Methods Maximizing Renyi's Entropy(Application)

Tetsuo Ichimori

Article type: Article
2012 Volume 22 Issue 3 Pages 81-96
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_81

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Apportionment is the distribution of house seats based proportionally on the population of electoral districts. It is impossible to meet the ideal of proportionality in practice because the number of seats given to each district must be an integer in apportionment. In fact, although there are a number of reasonable apportionment methods, it is not easy to evaluate them. This paper discusses the apportionment methods which maximize Renyi's entropy or minimize Renyi's divergence, where the values of each vote are considered a discrete probability distribution.

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An Image Analysis for Detecting Cancer Tissue via the algorithm Based on the Topology(Application)

Kazuaki Nakane, Marcio Gameiro, Takashi Suzuki, Nariaki Matsuura

Article type: Article
2012 Volume 22 Issue 3 Pages 97-108
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_97

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A pathological diagnosis is essential to treatment of cancer. Using a microscopy, a pathologist can decide the presence of cancer based on the altered morphologic appearance of tissue. The number of pathologists, however, does not match the number of patients. The fact that a few pathologists perform many diagnostics makes this process error prone. The development of pathological diagnosis assisted by computer is an urgent issue. In this paper, an algorithm based on the topological invariant is introduced and several results are shown. We have tried to test the colon tissue, the results are consistent with diagnosis by a pathologist.

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Numerical Stability of First Order Weak schemes for Storatonovich Stochastic Differential Equations

Yoshihiro Saito

Article type: Article
2012 Volume 22 Issue 3 Pages 109-116
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_109

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The numerical stability of first order weak schemes for the Stratonovich stochastic differential equations is discussed. We show that the Milstein and the Platen schemes have weak order 1. In this paper we study mean-square and asymptotic stability of Milstein and optimal Platen simplified schemes with a two point and uniformly distributed random variable which has similar moment properties to the normal random variable.

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On Convergence Behavior of the GMRES(m) Method with the Deflation-Type Restart and the Look-Back-Type Restart

Akira Imakura, Ji-Rong Yang, Tomohiro Sogabe, Shao-Liang Zhang

Article type: Article
2012 Volume 22 Issue 3 Pages 117-141
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_117

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We investigate two types of the improvement techniques for the GMRES(m) method to solve nonsymmetric linear systems: the deflation-type restart and the Look-Back-type restart. From the analysis based on the residual polynomials, we show in this paper that these restart techniques modify the convergence behavior of the GMRES(m) method by different mathematical backgrounds. Then under the knowledge from the analysis, we propose an efficient improvement of the GMRES(m) method with these restart techniques. The numerical experiments indicate that the proposed method shows the efficient convergence behavior.

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A Lagrangian Approach to Deriving Local-Energy-Preserving Numerical Schemes for the Euler-Lagrange Partial Differential Equations and an Application to the Nonreflecting Boundary Conditions for the Linear Wave Equation(Theory,<Special Topics>Activity Group "Scientific Computation and Numerical Analysis")

Takaharu Yaguchi

Article type: Article
2012 Volume 22 Issue 3 Pages 143-169
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_143

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We propose a Lagrangian approach to deriving local-energy-preserving finite difference schemes for the Euler-Lagrange partial differential equations regarding that, from Noether's theorem, the symmetry of time translation of Lagrangian yields the energy conservation law. We first observe that the local symmetry of time translation of Lagrangian derives the Euler-Lagrange equation and the energy conservation law, simultaneously. The new method is a combination of a discrete counter part of this statement and the discrete gradient method. As an application of the discrete local energy conservation law, we also discuss discretization of the nonreflecting boundary conditions for the linear wave equation.

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Finite Difference Approximation Requiring Function Values on Non-Grid Points(Theory,<Special Topics>Activity Group "Scientific Computation and Numerical Analysis")

Masahisa Tabata, Hirofumi Notsu

Article type: Article
2012 Volume 22 Issue 3 Pages 171-179
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_171

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We here investigate finite difference approximation requiring function values on non-grid points, while function values on grid points are employed in the conventional finite difference method. Such a finite difference approximation appears, for example, in deriving a finite difference scheme based on the method of characteristics for material derivative terms in flow problems. Introducing an interpolation operator to obtain the values on non-grid points, we evaluate the truncation error.

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Theoretical Analysis of Sinc Methods for Integral Equations of the Second Kind From a Practical Viewpoint(Survey,<Special Topics>Activity Group "Scientific Computation and Numerical Analysis")

Tomoaki Okayama

Article type: Article
2012 Volume 22 Issue 3 Pages 181-212
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_181

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Sinc methods for integral equations of the second kind have been actively developed since the early 2000s, and high efficiency of those schemes has been reported. In most of the schemes, however, there are two common points to be discussed: 1) it is difficult to implement those schemes unless the solution is given, and 2) convergence of the numerical solutions is not guaranteed. This situation is not desirable from a practical viewpoint. Recently, a remedy of these two points has been given by theoretical analysis. This paper is devoted to summarizing the researches about it.

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Structure-Preserving Numerical Methods for Differential Equations(Survey,<Special Topics>Activity Group "Scientific Computation and Numerical Analysis")

Takayasu Matsuo, Yuto Miyatake

Article type: Article
2012 Volume 22 Issue 3 Pages 213-251
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_213

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"Structure-preserving numerical methods" for differential equations are such special methods that preserve certain structures in differential equations. Since the concept had been raised in 1980's for ordinary differential equations, the subject has been extensively studied, and now the related studies have spreaded also to partial differential equations. In this survey, the elements of such methods are outlined, and some recent progresses are briefly described.

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[title in Japanese]

Article type: Appendix
2012 Volume 22 Issue 3 Pages App2-
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_App2

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[title in Japanese]

Article type: Appendix
2012 Volume 22 Issue 3 Pages App3-
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_App3

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[title in Japanese]

Article type: Appendix
2012 Volume 22 Issue 3 Pages App4-
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_App4

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[title in Japanese]

Article type: Cover
2012 Volume 22 Issue 3 Pages Cover3-
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_Cover3

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[title in Japanese]

Article type: Cover
2012 Volume 22 Issue 3 Pages Cover4-
Published: September 25, 2012
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.22.3_Cover4

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