Transactions of the Japan Society for Industrial and Applied Mathematics

[title in Japanese]

Article type: Cover
1992 Volume 2 Issue 1 Pages Cover1-
Published: March 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.1_Cover1

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[title in Japanese]

Article type: Cover
1992 Volume 2 Issue 1 Pages Cover2-
Published: March 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.1_Cover2

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[title in Japanese]

[in Japanese]

Article type: Article
1992 Volume 2 Issue 1 Pages i-
Published: March 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.1_i

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Discrete approximation for stochastic differential equations

Yoshihiro Saito, Taketomo Mitsui

Article type: Article
1992 Volume 2 Issue 1 Pages 1-16
Published: March 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.1_1

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Stochastic differential equations(SDEs), which appear in various fields of applications, e.g. statistical physics and population dynamics, require another way of calculus than that in usual deterministic case. Among discrete approximations for deterministic differential equations(DDEs), Runge-Kutta method(RK method) is well known. This paper presents a stochastic version of RK method and its applicability for scalar stochastic differential equation. However the local order of convergence of RK scheme in mean-square sense is known to be bounded by 2 in scalar case. We give a way to improve the local order for 3-stage RK scheme.

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Error Analysis of Gregory's and Bickley's Formulas

Kazuo Hatano

Article type: Article
1992 Volume 2 Issue 1 Pages 17-54
Published: March 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.1_17

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Among numerical quadrature formulas the simplest one is the trapezoidal rule or the mid-point rule. Gregory's/Bickley's formula can be regarded as the trapezoidal/mid-point rule with correction expressed in terms of differences. These formulas are classical and simple, but their truncation errors have not yet been analyzed thoroughly. In this paper, we introduce Gregory's and Bickley's formulas with integral remainders, which are the direct application of Markoff's formula to the Euler-Maclaurin summation formula and to the second Euler-Maclaurin summation formula, respectively. Based on these remainders, we can get the error bound of these formulas. The round-off errors are also discussed. Some numerical examples are also shown.

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Optimal regularization for ill-posed problems by means of L-curve

YOHSUKE HOSODA, TAKASHI KITAGAWA

Article type: Article
1992 Volume 2 Issue 1 Pages 55-67
Published: March 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.1_55

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In this paper we propose a new method to estimate the optimal regularization parameter. It is observed numerically that the corner of L-curve which is proposed by P.C. Hansen gives a clue for the selection of the parameter [6]. We introduce a function which represents the curvature of the L-curve whose maximizer gives a good estimation of the parameter.

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ON THE GLOBAL BEHAVIOR OF ONE PARAMETER FAMILIES OF ITERATION METHODS FOR ALGEBRAIC EQUATIONS

MASAO IGARASHI

Article type: Article
1992 Volume 2 Issue 1 Pages 69-78
Published: March 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.1_69

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We consider a one parameter family of iteration methods for finding zeros of algebraic equations. The family includes the second order Newton-Raphson's, third order Halley's and modified Newton-Raphson's methods. Investigation of the relationship between the number of iteration times and the parameter value reveals that the computational efficiency of the iteration methods should be evaluate in terms of the global behavior of the methods. The conclusion obtained are also applicable to other one parameter families, such as the one introduced by E. Hansen and M.Patrick. Numerical examples are included.

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Higher Accurate Symplectic Finite Difference Schemes Constructed from The Canonical Transform

Toshiaki Itoh, DongSheng Cai

Article type: Article
1992 Volume 2 Issue 1 Pages 79-90
Published: March 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.1_79

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Some schemes for constructing symplectic finite difference equations are developed. New procedures presented in this paper generate interesting finite difference schemes which are called a symplectic integration algorithm(SIA). We can show that schemes genereted from the procedure have a mixed form as the well known Leap-Frog and Discrete Mechanical scheme.

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Exact Computation of Jordan Normal Forms of Matrices by Computer Algebra

Shuichi Moritsugu, Kazuko Kuriyama

Article type: Article
1992 Volume 2 Issue 1 Pages 91-103
Published: March 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.1_91

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In this paper, algorithms for computing Jordan Normal Forms of square matrices over the rational number field are elucidated. The computation is exactly carried out by computer algebra, and the result is free from any numerical errors. These algorithms are deduced from well-known mathematical theorems, but they have not been installed yet in most of computer algebra system. Basic algorithms contain the step of solution of algebraic equations, which limits the applicability of the program. Theorefore, the improvement of the defect is discussed. The result of experimental implementation on REDUCE3.3 shows that the improved algorithm works quite efficiently.

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[title in Japanese]

Article type: Appendix
1992 Volume 2 Issue 1 Pages App1-
Published: March 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.1_App1

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[title in Japanese]

Article type: Cover
1992 Volume 2 Issue 1 Pages Cover3-
Published: March 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.1_Cover3

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[title in Japanese]

Article type: Cover
1992 Volume 2 Issue 1 Pages Cover4-
Published: March 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.1_Cover4

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