Transactions of the Japan Society for Industrial and Applied Mathematics

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

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Volume 17, Issue 1

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[title in Japanese]

Article type: Cover
2007 Volume 17 Issue 1 Pages Cover1-
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_Cover1

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[title in Japanese]

Article type: Cover
2007 Volume 17 Issue 1 Pages Cover2-
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_Cover2

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[title in Japanese]

Article type: Appendix
2007 Volume 17 Issue 1 Pages App1-
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_App1

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[title in Japanese]

[in Japanese]

Article type: Article
2007 Volume 17 Issue 1 Pages A1-
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_A1

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[title in Japanese]

Article type: Appendix
2007 Volume 17 Issue 1 Pages i-xxix
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_i

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Geometric Structures of Neural Networks in a Function Space

Masaharu ISHII

Article type: Article
2007 Volume 17 Issue 1 Pages 1-26
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_1

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In this paper, we set some assumptions for properties of neurons and study global structure of neurovarieties in a function space of 3-layered neural-networks by using these properties. Firstly we determine structure of regular points in neurovarieties as a submanifold of the function space by particularly using one of the properties "differentially strong non-degeneracy". Next we show a distribution of all singular points in the neurovarieties and internal structure of the singular points. Furthermore we show by using one of the properties "approximate degeneracy" that neurovarieties have folded structure.(Theory)

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Extension of the MRTR method for solving complex symmetric linear systems

Akira SHIODE, Kuniyoshi ABE, Seiji FUJINO

Article type: Article
2007 Volume 17 Issue 1 Pages 27-42
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_27

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The MRTR method has been recognized as an effective iterative method for singular systems of linear equations. The MRTR method is based on the three-term recurrence formula of the CG method and the algorithm is proven to be mathematically equivalent to the CR method. In this paper, we extend the MRTR method to solve complex symmetric linear systems. We describe this extended cs_MRTR method and prove that this method is mathematically equivalent to the COCR method. Numerical examples show that the cs_MRTR method shows a more stable convergence behavior than the COCR method.(Theory)

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An Implicit Numerical Method for Fractional Diffusion Equations

Toshiyuki Koto

Article type: Article
2007 Volume 17 Issue 1 Pages 43-58
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_43

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This paper is concerned with a numerical method for solving a model equation of anomalous diffusion expressed with fractional integral with respect to the time variable t. In particular, a semi-discretization scheme derived from the application of the fractional trapezoidal rule proposed by Lubich in the mid 80's to the integral is examined. It is verified that the scheme converges in a special case where the exact solution is represented in a generalized Taylor form in fractional powers of t. Numerical examples are also presented which suggest convergence of the scheme in more general cases.(Theory)

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Effects of the window in information on fitting a chaotic time series to a stochastic long memory process

Kei Inoue

Article type: Article
2007 Volume 17 Issue 1 Pages 59-72
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_59

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It is known that a certain chaotic deterministic process exhibits long memory behavior. Recently, Guegan shows how we can adjust such a chaotic time series to a stchastic long memory process. He estimated a value for long memory parameter of a chaotic time series with long memory. In this paper, we introduce a periodogram smoothed by the window in information. We attempt to reduce the estimated error of a spectral density.(Application)

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[title in Japanese]

Article type: Appendix
2007 Volume 17 Issue 1 Pages App2-
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_App2

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[title in Japanese]

Article type: Appendix
2007 Volume 17 Issue 1 Pages App3-
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_App3

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[title in Japanese]

Article type: Cover
2007 Volume 17 Issue 1 Pages Cover3-
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_Cover3

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[title in Japanese]

Article type: Cover
2007 Volume 17 Issue 1 Pages Cover4-
Published: March 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.1_Cover4

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