Transactions of the Japan Society for Industrial and Applied Mathematics

Transactions of the Japan Society for Industrial and Applied Mathematics

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

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Volume 9, Issue 1

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[title in Japanese]

Article type: Cover
1999 Volume 9 Issue 1 Pages Cover1-
Published: March 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.1_Cover1

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[title in Japanese]

Article type: Cover
1999 Volume 9 Issue 1 Pages Cover2-
Published: March 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.1_Cover2

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[title in Japanese]

Article type: Appendix
1999 Volume 9 Issue 1 Pages App1-
Published: March 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.1_App1

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[title in Japanese]

[in Japanese]

Article type: Article
1999 Volume 9 Issue 1 Pages i-
Published: March 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.1_i

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[title in Japanese]

Article type: Appendix
1999 Volume 9 Issue 1 Pages App2-
Published: March 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.1_App2

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Convergence Theory of the CR Method for Linear Singular Systems

Kuniyoshi ABE, Hidenori OGATA, Masaaki SUGIHARA, Shao-Liang ZHANG, Tak ...

Article type: Article
1999 Volume 9 Issue 1 Pages 1-13
Published: March 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.1_1

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The convergence rate of the residual vector of the conjugate residual (CR) method is well known for a linear system Ax=b, where A is nonsingular. In this paper, we consider the convergence theory of the CR method for a linear system, where the coefficient matrix is singular. First, when we give a certain condition, we show that the algorithm of the CR method can be decomposed into components in the range space of A, which we denote by R(A), and the orthogonal complement space of R(A). Secondly, we present a bound of the residual norms of the CR method in R(A). These two results imply that we can derive an estimate of the error bound for a linear singular system. Moreover, we show necessary and sufficient conditions for the convergence of the CR method starting with an arbitrary right-hand side vector. As a byproduct, the residual norm of the CR method for symmetric positive semi-definite coefficient matrices is also analyzed.

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On Lower Bounds for Network Reliability by Series-parallel Graphs

Takeshi KOIDE, Shuichi SHINMORI, Hiroaki ISHII

Article type: Article
1999 Volume 9 Issue 1 Pages 15-35
Published: March 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.1_15

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A simplified model for a communication network is a probabilistic graph where no node fails but each edge operates with a probability. One of the indicators which measure the performance of the network is all-terminal reliability, that is, the probability that all nodes are connected with operational edges. Since it is #P-complete to calculate the value of the all-terminal reliability precisely, it is important to obtain its bound efficiently. In [29], we have proposed a polynomial time algorithm that derives the lower bound by using edge-packing consisting of spanning trees. They have a great merit that they can be applied to the probabilistic graphs where each edge operates with a different probability. In this paper, we propose new algorithms by using edge-packing consisting of series-parallel subgraphs. The algorithms derive tighter lower bounds without losing the above merit.

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[title in Japanese]

Article type: Appendix
1999 Volume 9 Issue 1 Pages App3-
Published: March 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.1_App3

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[title in Japanese]

Article type: Cover
1999 Volume 9 Issue 1 Pages Cover3-
Published: March 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.1_Cover3

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[title in Japanese]

Article type: Cover
1999 Volume 9 Issue 1 Pages Cover4-
Published: March 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.1_Cover4

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