Transactions of the Japan Society for Industrial and Applied Mathematics

[title in Japanese]

Article type: Cover
1997 Volume 7 Issue 1 Pages Cover1-
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_Cover1

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[title in Japanese]

Article type: Cover
1997 Volume 7 Issue 1 Pages Cover2-
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_Cover2

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[title in Japanese]

[in Japanese]

Article type: Article
1997 Volume 7 Issue 1 Pages i-
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_i

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Parallel Block Methods of Predictor-Corrector Type and Its Stepsize Strategy

Susumu Yamada, Kazufumi Ozawa

Article type: Article
1997 Volume 7 Issue 1 Pages 1-26
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_1

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Parallel block methods with a stepsize strategy are developed for solving nonstiff initial value problems on parallel computers. The block methods use the predictor-corrector iteration, which makes it easy to exploit "parallelism across the method" for the solutions of nonlinear equations. The stepsize strategy used in the methods is based on Milne's device which estimates the local error using the predicted and corrected values. Numerical experiments are carried out on a KSR1 parallel computer in order to show the performance of the block methods. The computational costs, errors and speed-up ratios of the block methods are compared with those of the PIRK(parallel iterated Runge-Kutta) by Houwen et al.

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Derivation of transport equations for the analysis of variable composition semiconductor devices at low-temperatures

Hideyuki Iwata, Takashi Ohzone

Article type: Article
1997 Volume 7 Issue 1 Pages 27-36
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_27

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Transport equations for use in analysis of not only homogenous but also variable composition semiconductor devices at low-temperatures are systematically derived. In these equations, Fermi-Dirac statistics and position-dependent band structure are taken into account. The general transport equations in materials with nonuniform band structure of previous workers are recast into a simple form so as to be convenient for use in numerical device simulation of those semiconductors at low-temperatures.

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MRTR Method : An Iterative Method Based on the Three-Term Recurrence Formula of CG-Type for Nonsymmetric Matrix

Kuniyoshi ABE, Shao-Liang ZHANG, Taketomo MITSUI

Article type: Article
1997 Volume 7 Issue 1 Pages 37-50
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_37

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The residual polynomial of GPBi-CG method is represented in the product of the Lanczos polynomial R_k(A), the polynomial H_k(A) similar to the Lanczos but different in parameters, and the starting residual vector. We remove R_k(A) from the residual polynomial, namely, we suggest a new method whose residual vector is the product of the starting one and H_k(A) only. The algorithm, which is called MRTR method, is proven to be mathematically equivalent to the conjugate residual(CR)method. Therefore, we can show its convergence as well as its error bound. However, MRTR method is different from CR method in their implementation. MRTR method has less operation cost than CR method per iteration step. Through numerical experiments of nonsingular and singular linear equations we confirm the equivalence on numerical computations. Moreover, we show that MRTR method is more effective than CR method.

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Traffic Assignment Problem Considering the Toll of Expressway : a Model and an Algorithm

Kazumiti Numata, Hirofumi Nonotoh

Article type: Article
1997 Volume 7 Issue 1 Pages 51-64
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_51

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We consider the traffic assignnment problem on road networks consisting of ordinary roads and express tollways. Existing models of the traffic assignment under the principle of "user optimization" have treated a travel time as the only cost considered by travellers. In this paper we present a model in which both the travel time and the expressway tolls are considered, and formulate it as a mathmatical programming problem. Then, for this problem, we propose a simple algorithm based on the column generation technique and show some numerical results of this proposed algorithm applied to small scale problems.

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Estimation of Locations and Magnitudes of Point Sources for Multidimensional Poisson Equation

Katsu Yamatani, Kohzaburo Ohnaka

Article type: Article
1997 Volume 7 Issue 1 Pages 65-78
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_65

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This papar discusses an inverse source problem for multidimensional Poisson equation. The source term is expressed by a sum of several point sources. We propose a reliable method to estimate unknown locations and magnitudes of point sources under the condition that the potential and flux are observed on the boundary. Our method is based on a weighted residual approach using harmonic functions for weighting functions and need not use a direct analysis for the governing equation. The effectiveness of the method is illustrated with numerical examples.

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On the Round-off Error Estimation Using IEEE754 Floating-Point Arithmetic

Tomonori Kouya, Hideko Nagasaka

Article type: Article
1997 Volume 7 Issue 1 Pages 79-89
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_79

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We propose the round-off error estimation using IEEE754 floating-point arithmetic which widely used on various workstations and personal computers. Interval Analysis is one of the standard methods in order to estimatite round-off errors in numerical processes, but it is not more convenient for a lot of users. In this paper, we explain the proposed estimation and show the source programs which can run on SparcStaion, PC-9801 and IBM PC/AT compatible. Finally, numerical experiments demonstrate the effectiveness of the proposed estimation.

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On Some Practical Criteria for Positive Definite Matrices

LEI LI

Article type: Article
1997 Volume 7 Issue 1 Pages 91-96
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_91

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This paper presents some practical criteria for the positive definite matrices. They are applicable to wider situations and are easy to check than other criteria now in common use.

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[title in Japanese]

Article type: Appendix
1997 Volume 7 Issue 1 Pages App1-
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_App1

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[title in Japanese]

Article type: Cover
1997 Volume 7 Issue 1 Pages Cover3-
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_Cover3

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[title in Japanese]

Article type: Cover
1997 Volume 7 Issue 1 Pages Cover4-
Published: March 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.7.1_Cover4

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