Transactions of the Japan Society for Industrial and Applied Mathematics

[title in Japanese]

Article type: Cover
1994 Volume 4 Issue 3 Pages Cover1-
Published: September 15, 1994
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.4.3_Cover1

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[title in Japanese]

Article type: Cover
1994 Volume 4 Issue 3 Pages Cover2-
Published: September 15, 1994
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.4.3_Cover2

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[title in Japanese]

[in Japanese]

Article type: Article
1994 Volume 4 Issue 3 Pages i-
Published: September 15, 1994
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.4.3_i

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Statistical Manifold of Infinite Dimension

Toru Kambayashi

Article type: Article
1994 Volume 4 Issue 3 Pages 211-228
Published: September 15, 1994
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.4.3_211

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This is an attempt to establish a framework of infinite dimensional information geometry. The space of the probability densikties on [0.1] which are absolutely continuous and the derivatives of which are square integrable is considered. The space is an open Hilbert manifold. The Fisher metric, however, is not compatible with the topology of the manifold. The unique existence of the covariant derivative which is metric and torsion free is proved, and the equation of the geodesic is shown. The equation is explicitly solved. It is proved that the manifold has some desirable geometrical characters.

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A FAST AND PARALLEL ALGORITHM FOR SOLVING A CLASS OF BLOCK TRIDIAGONAL LINEAR SYSTEMS

Lei LI, Tadao NAKAMURA

Article type: Article
1994 Volume 4 Issue 3 Pages 229-234
Published: September 15, 1994
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.4.3_229

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We consider solving equations Mx=b with following the block tridiagonal coefficient matrix [chemical formula] where A_1, B_1, and C_1 are all n×n matrices, and there exists a constant matrix G, G is satisfied with a)GA_j=A_jG, j=1〜m, GB_j=B_jG, j=1〜m-1, GC_j=C_jG, j=2〜m. b)G has n distinct eigenvalues. In this paper, we present a fast and parallel direct method for solving this linear systems. If the operation time to reduce G into Jordan canonical form is disregarded, then this method takes 10mn^2+8mn-4n^2 arithmetic operations at most. And the number of parallel steps of this method is O(log_2N) at most by using mn^2 processors, where N=max(m, n). Specially, for the linear systems which is got by disturbing the diagonal elements of coefficient matrix of Poisson difference equations, the number of arithmetic operations of this method is O(mnlog_2n) at most by using FFT algorithm. And the number of its parallel steps is O(log_2N) at most by uising mn processoes, where N=max(m, n).

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Solution of Minimax Problems via Approximation by p-th Power Sum and its Applications to Geometric Problems

Sigeru Ando

Article type: Article
1994 Volume 4 Issue 3 Pages 235-250
Published: September 15, 1994
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.4.3_235

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This paper presents an iterative method for some class of minimax problems, namely "Minimize max_kf_k(x)", based on the fact that max_kf_k(x)is, with p large enough, approximated by (Σ_kf_k(x)^p)^<1/p>which is a smooth function, and hence can be minimized by means of Newton's iteration ; and also dicusses its applications to problems in computational geometry.

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A Note on the Durand-Kerner Method

Tetsuro Yamamoto, Sachio Kanno

Article type: Article
1994 Volume 4 Issue 3 Pages 251-258
Published: September 15, 1994
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.4.3_251

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The Durand-Kerner method is one of central techniques for finding all the zeros of a polynomial simultaneously. Interesting properties on this method have been obtained by several authors. In this paper, it is shown that some of them can be derived from the well known Lagrangian interpolation formula. Some remarks are also added.

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Two-step comulative curve and modified Gompertz curve

Kunio Oshima, Ichiro Hofuku, Akira Inagawa

Article type: Article
1994 Volume 4 Issue 3 Pages 259-274
Published: September 15, 1994
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.4.3_259

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In general, the cumulative curves of the bugs agree with Gompertz curve or Logistic curve in many software developments. Using these curves, we will be able to forcast the total number of the bugs when we estimate them within the certain interval. But many experiments show us that those estimates do not coincide with the actual number of bugs. In our experimental data, the se curves usually have more than two steps(a step means an interval or a point where the socond derivative is zero in terms of a continuous function), In this paper, we will study the following four problems ; ・to give the analogy for debugging processes and to find several reasons why such curves appear by means of Gray box method. ・to define a continuous function which is called a modified Gompertz curve that can be expressed by more than two steps. ・to fit the modified Gompertz curve for such a cumulative curve which has more than two steps. ・to forcast total number of bugs on the first step by fitting the modefied Gompertz curve.

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[title in Japanese]

Article type: Appendix
1994 Volume 4 Issue 3 Pages App1-
Published: September 15, 1994
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.4.3_App1

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[title in Japanese]

Article type: Cover
1994 Volume 4 Issue 3 Pages Cover3-
Published: September 15, 1994
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.4.3_Cover3

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[title in Japanese]

Article type: Cover
1994 Volume 4 Issue 3 Pages Cover4-
Published: September 15, 1994
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.4.3_Cover4

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