Transactions of the Japan Society for Industrial and Applied Mathematics

[title in Japanese]

Article type: Cover
1991 Volume 1 Issue 4 Pages Cover1-
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_Cover1

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[title in Japanese]

Article type: Cover
1991 Volume 1 Issue 4 Pages Cover2-
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_Cover2

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[title in Japanese]

[in Japanese]

Article type: Article
1991 Volume 1 Issue 4 Pages i-
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_i

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Optimal State Assignment for Sequential Circuits by High-Speed Design Methodology

Motonobu Tonomura

Article type: Article
1991 Volume 1 Issue 4 Pages 263-275
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_263

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This paper presents a design methodology for high-speed sequential circuits. As high-density integrated circuit technology advances, the number of transistor cells in a circuit is becoming unimportant. To minimize the circuit depth, it is necessary to find locally dependent information. A transition graph representation of partition pairs is obtained from state sets of a sequential circuit, using the concept of multi-block partitions. An algorithm is proposed for minimizing the code length in the minimum logic depth of the state transition functions, by efficiently dividing multi-block partitions into two blocks.

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Numerical Factorization of Polynomial by the Divide and Conquer Method

Shingo Sonoda, Tetsuya Sakurai, Hiroshi Sugiura, Tatsuo Torii

Article type: Article
1991 Volume 1 Issue 4 Pages 277-290
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_277

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We paper an iterative formula for factorizing a high degree polynomial into two polynomials numerically by solving some congruent equation with the aid of Euclidian algorithm. This polynomial factorization gives a fast algorithm as the name of a divide and conquer method for simultaneous calculation of all the zeros of a polynomial.

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A 3-Stage Fourth Order RK Formula for Parallel Computers

Akira Goto, Taketomo Mitsui

Article type: Article
1991 Volume 1 Issue 4 Pages 291-304
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_291

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We made a new A-stable 3-stage fourth order Runge-Kutta formula which can be calculated in parallel. Our matrix A, whose components identify an IRK formula together with the vector b, and its eigenvalues can be expressed in a closed algebraic form. The diagonalization of A is a crucial point for our parallel algorithm. The eigenvalues of A should be greater than 1/2 for the A_0-stability. However we find that the smaller the eigenvalue of A is, the more accurate the solution of the parallelized IRK is.

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A Generalization of the Simultaneous Diagonalization of Hermitian Matrices and Its Relation to Quantum Estimation Theory

Hiroshi Nagaoka

Article type: Article
1991 Volume 1 Issue 4 Pages 305-318
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_305

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We study the problem of minimizing a quadratic quantity defined for given two Hermitian matrices X, Y and a positive-definite Hermitian matrix. This problem is reduced to the simultaneous diagonalization X, Y when XY=YX. We derive a lower bound for the quantity, and in some special cases solve the problem by showing that the lower bound is achievable. This problem is closely related to a simultaneous measurement of quantum mechanical observables which are not commuting and has an application in the theory of quantum state estimation.

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Study on the Convergence Characteristics of methods of Multigrid and ADI

Mitsuyoshi Igai, Toshio Okouchi, Chisato Konno

Article type: Article
1991 Volume 1 Issue 4 Pages 319-332
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_319

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On the purpose of developing a matrix solver on massively parallel computers (MPC), we have investigated the both Multigrid and ADI method, and had numerical experiments, applying them to practical problems (2-D Poisson equation with Neumann type boundary conditions, etc). We show that Multigrid method is as efficient as ILUBCG on the scalar processor, required operations for ADI method is around 10 times the size for ILUBCG on the scalar processor, ADI method is especially powerful for the convective diffusion problems, and an effective acceleration factor in a uniform diffusion field is not available for a non-uniform field. We have concluded that they will be useful enough on MPC because of their large granularity.

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Use of Derivatives at Endpoints in Romberg Integration

Hideo Toda, Harumi Ono, Masao Iri

Article type: Article
1991 Volume 1 Issue 4 Pages 333-344
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_333

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Numerical methods using derivatives have been considered until recently to be disadvantageous. However, since automatic methods for simultaneous computation of functions and partial derivatives are now available, we may make more use of derivatives in various fields of numerical methods. From this standpoint, we consider the complexity of new variants of the Romberg integration, which require the derivatives only at both endpoints. Among these variants, the method using the first derivatives is one of the most promising with respect to the amount of computational work, because it achieves the same accuracy as the standard Romberg integration with half stepsize.

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Suppression of Fourier coefficients by appending of rapidly decreasing functions

Yasuyo Hatano

Article type: Article
1991 Volume 1 Issue 4 Pages 345-359
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_345

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This paper presents a new method to decrease Fourier coefficients of higher orders for observed data. Rapidly decreasing function, x^m(ax+b), is appended to both ends of given data. The merits of this method have an objective criterion for minimizing Fourier coefficients of the higher orders, and gives the reliable results. Simple numerical examples and numerical applications are also shown.

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The Tracing of The Equilibrium Curve of A Non-linear System by Using The Coordinate Transformation

Yoshihiko Kataoka

Article type: Article
1991 Volume 1 Issue 4 Pages 361-373
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_361

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This paper deals with the tracing of the equilibium curve of a non-linear system by using the coodinate transformation. The apparent regularity of a model of a non-linear system near and at the saddle-node bifurcation point is improved locally by coordinate transformation. The global tracing including saddle-node bifurcation point is realized by revising the coodinate transformation on the way of tracing the curve. The efficiency of the method is shown in practical large scale system.

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[title in Japanese]

Article type: Index
1991 Volume 1 Issue 4 Pages Toc1-
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_Toc1

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[title in Japanese]

Article type: Index
1991 Volume 1 Issue 4 Pages Index1-
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_Index1

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[title in Japanese]

Article type: Appendix
1991 Volume 1 Issue 4 Pages App1-
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_App1

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[title in Japanese]

Article type: Cover
1991 Volume 1 Issue 4 Pages Cover3-
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_Cover3

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[title in Japanese]

Article type: Cover
1991 Volume 1 Issue 4 Pages Cover4-
Published: December 15, 1991
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.1.4_Cover4

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