Transactions of the Japan Society for Industrial and Applied Mathematics

Online ISSN : 2424-0982
ISSN-L : 0917-2246

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Volume 2, Issue 3

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[title in Japanese]

Article type: Cover
1992 Volume 2 Issue 3 Pages Cover1-
Published: September 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.3_Cover1

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[title in Japanese]

Article type: Cover
1992 Volume 2 Issue 3 Pages Cover2-
Published: September 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.3_Cover2

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[title in Japanese]

[in Japanese]

Article type: Article
1992 Volume 2 Issue 3 Pages i-
Published: September 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.3_i

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Maximum Likelihood Parameter Estimation of Discrete Fractional Gaussian Noise Based on the Asymptotic Diagonalization of Covariance Matrix

Masahiro Itonaga

Article type: Article
1992 Volume 2 Issue 3 Pages 145-154
Published: September 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.3_145

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An efficient procedure based on the asymptotic diagonalization of covariance matrix is proposed to obtain the approximate maximum likelihood estimate (MLE) of parameters of the discrete fractional Gaussian noise. Since this procedure can be executed using the FFT method, it requires an extremely cheaper computational cost than the procedure to acquire the exact MLE which is to some extent efficiently performed using the Levinson algorithm. It is found from numerical experiments that the mean square error (MSE) of the approximate MLE based on the proposed procedure is comparable to the MSE of the exact MLE and nearly attains to the Cramer-Rao lower bound when N (number of data points) ≳10^2.

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The Architecture of A Programming Language LAMAX-S Oriented for the Mathematical Characteristics of Matrix, And Its Processor.

Satoshi Uchida, Naokazu Yamaki, Shigeru Hongo, Yoshiaki Inoue, Yutaka ...

Article type: Article
1992 Volume 2 Issue 3 Pages 155-168
Published: September 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.3_155

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This paper presents a new programming language for matrix calculation LAMAX-S(LAnguage for MAtriX calculation - Supercomputer). In LAMAX-S, 9 kinds of matrix form can be described such as band matrix, triangular matrix and diagonal matrix. And two additional attributes can be described: (1) a specific form such as symmetric, sparse. (2) Mathematical condition such as positive definite. LAMAX-S preprocessor translates LAMAX-S source program to FORTRAN based on the mathematical description. In this paper, we presents a design of LAMAX-S from a mathematical point of view and its prototype.

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An Explicit Form of the Minimum Eigenvalue of the One-Dimensional Heat Equation

Kazuo Arai, Tomohiro Marui, Satosi Maruyama

Article type: Article
1992 Volume 2 Issue 3 Pages 169-175
Published: September 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.3_169

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This note presents a practical approximation method for computing the minimum eigenvalue for a transcendental equation derived from the heat equation with a convective boundary condition. The transcendental equation is approximated by a finite continued fraction equation, which is a quadratic equation. Its solution(the minimum eigenvalue ) is obtained in a closed form depending explicitly on the Biot number. The method is faster than the conventional Newton method and the error is within 0.3%, a level that is quite satisfactory for practical use.

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Novel Formulas for Numerical Computation of Toroidal Function of the Second Kind

Takashi Tsumagari

Article type: Article
1992 Volume 2 Issue 3 Pages 177-191
Published: September 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.3_177

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We propose two kinds of novel formulas for calculating the toroidal function (TF) of the second kind. The first formula, which is applicable to the TF of low degree, has the superior performance with respect to computation time (about 0.5 ms on a 486SX based PC). The second has been formulated by using the technique of Landen's transformation for complete elliptic integrals. We confirmed on the same machine that TF of degree 50 can be calculated by the our second formula in the reasonable computation time. Proposed formulas will apply to the numerical computation of electric fields.

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[title in Japanese]

Article type: Appendix
1992 Volume 2 Issue 3 Pages App1-
Published: September 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.3_App1

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[title in Japanese]

Article type: Cover
1992 Volume 2 Issue 3 Pages Cover3-
Published: September 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.3_Cover3

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[title in Japanese]

Article type: Cover
1992 Volume 2 Issue 3 Pages Cover4-
Published: September 15, 1992
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.2.3_Cover4

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