Transactions of the Japan Society for Industrial and Applied Mathematics

[title in Japanese]

Article type: Cover
1995 Volume 5 Issue 4 Pages Cover1-
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_Cover1

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[title in Japanese]

Article type: Cover
1995 Volume 5 Issue 4 Pages Cover2-
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_Cover2

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[title in Japanese]

[in Japanese]

Article type: Article
1995 Volume 5 Issue 4 Pages i-
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_i

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A Class of Product-type Methods Based on Lanczos Process

SHAO-LIANG ZHANG, SEIJI FUJINO

Article type: Article
1995 Volume 5 Issue 4 Pages 343-360
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_343

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In this paper, we propose a unification of results involving product-type methods for the iterative solution of nonsymmetric linear systems. A characteristic of this class of methods(that includes CGS. Bi-CGSTAB, and Bi-CGSTAB2)is the relationship γ_n=H_n(A)R_n(A)γ_0 where γ_n is the residual vector corresponding to the n-th iterate x_n, and R_n is the Lanczos polynomial generated from Bi-CG. The poly-nomial H_n in the product H_n(A)R_n(A) is chosen to speed up and/or stabilize convergence, while satisfying a standard three-term recurrence relations. Such product-type methods can be regarded as generalizations of Bi-CGSTAB. From the unification, we can see how CGS, Bi-CGSTAB, and Bi-CGSTAB2 fit into a more general framework.

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Analysis of Parallelism and Efficiencies of BDF Type Block Methods

Susumu Yamada, Kazufumi Ozawa, Hisashi Nara

Article type: Article
1995 Volume 5 Issue 4 Pages 361-379
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_361

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Parallel block methods of BDF(backward differentiation formulae)type are studied for solving stiff differential equations. In order to treat errors of parallel and serial methods on a unified basis, the parallel block methods are reformulated in the form of the general linear method, which leads to a natural definition of global errors. The computational costs, errors and speed-up ratios of the proposed block methods are compared with those of the conventional BDF. It showld be noted that there exists an efficient method which reduces the computational cost of the conventional BDF of the same order by a factor of 5 using only two processors. The reason of the achievement is discussed. Experimental results which demonstrate the validity of the theoretical analysis are presented.

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An Algorithm for Finding a Shortest Pair of Paths in a Plane Region

Yoshiyuki Kusakari, Hitoshi Suzuki, Takao Nishizeki

Article type: Article
1995 Volume 5 Issue 4 Pages 381-398
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_381

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Given axis-parallel rectangular obstacles and crossing areas together with two pairs of terminals on the plane, our algorithm finds a shortest pair of rectilinear paths which connect the pairs of terminals and neither pass through any obstacles nor cross each other except in the crossing areas. The algorithm takes O(n log n)time and O(n)space, where n is the total number of obstacles and crossing areas.

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Parallel Computing Algorithms of Neural Networks on an 8-neighbor Processor Arrays

Toshihiro Taketa, Akiyoshi Tanaka, Kuninobu Tanno

Article type: Article
1995 Volume 5 Issue 4 Pages 399-409
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_399

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Various types of neural networks have been proposed, and many applications of the technology have also been vigorously promoted in the wide range of the fields. However, simulations of large scale neural networks require quite high speed computation ability because of an enormous of time in learning. Then, many studies have been reported on efficient parallel simulation of neural networks. This paper proposes parallel computing algorithm allowing the back-propagation model to be simulated upon an 8-neighbor processor array. Taking account of the parallelism intrinsically imbedded in the neural networks, the algorithm realizes high speed neural network computation. The time complexities of the algorithm are only O(NLp/P)for communications and O(N^2L/P)for computation in one step learning processing, where N is the number of the neurons in a layer, P(pxp)is the number of processors, and L is the number of the layers.

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Finite Difference Approximation Method to Mean Curvature Flow Equation and the Criterion in Image Processing

Daisuke Hirata, Masayoshi Tsutsumi

Article type: Article
1995 Volume 5 Issue 4 Pages 411-422
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_411

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This paper presents a new finite difference method for image restoration based on mean curvature flow equation. The algorithm is the fastest as possible on account of the explicit form. We give a proof of the L^∞ stable condition and show numerical results. Moreover we propose a criterion for comparison with those introduced by a previous method.

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Computational Method of Particle Trajectories for Conserving Adiabatic Invariants in Discrete Electro-Magnetic Fields

Tohru Shimizu, Masayuki Ugai

Article type: Article
1995 Volume 5 Issue 4 Pages 423-444
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_423

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When charged particle trajectories are numerically calculated in discrete electro-magnetic fields obtained from computer simulations, it is necessary to interpolate spatially the field data. Usually, linear interpolation has been used for this purpose, but in this case adiabatic invariants are not conserved for the calculated particle trajectory. We hence propose an interpolation method, by which the solenoidal condition of magnetic field is exactly satisfied. The adiabatic invariants are conserved for particle trajectories calculated in the resulting continuous fields, and the use of the lowest order interpolation scheme demands cpu time only little more than the case of linear interpolation. This method is applied to two test magnetic fields of simple topology and a complicated electro-magnetic field data obtained from MHD simulation. It is argued that in order to calculate particle trajectories correctly magnetic field data should be interpolated so that the solenoidal condition is satisfied. It is also argued that this method is applicable to general plasma particle simulations.

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Proposition of Recursive Distribution Method for Probabilistic Fracture Mechanics

Hiroshi AKIBA, Shinobu YOSHIMURA, Genki YAGAWA

Article type: Article
1995 Volume 5 Issue 4 Pages 445-461
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_445

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This paper proposes a new method for Probabilistic Fracture Mechanics(PFM). The present method gives a time-evolution law of a probability measure or a bounded Lebesgue-Stieltjes measure induced by a joint distribution function of a crack geometry, which is obtained from initial random variables and a deterministic time-evolution law of the variables. A numerical example of a Light Water Reactor(LWR)'s piping problem is solved by the present method and the results are compared with those of the Monte Carlo(MC)method. Both results agree sufficiently well, while CPU time of the present method is remarkably short.

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[title in Japanese]

Article type: Index
1995 Volume 5 Issue 4 Pages Toc1-
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_Toc1

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[title in Japanese]

Article type: Index
1995 Volume 5 Issue 4 Pages Index1-
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_Index1

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[title in Japanese]

Article type: Appendix
1995 Volume 5 Issue 4 Pages App1-
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_App1

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[title in Japanese]

Article type: Cover
1995 Volume 5 Issue 4 Pages Cover3-
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_Cover3

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[title in Japanese]

Article type: Cover
1995 Volume 5 Issue 4 Pages Cover4-
Published: December 15, 1995
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.5.4_Cover4

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