Transactions of the Japan Society for Industrial and Applied Mathematics

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

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Volume 20, Issue 2

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[title in Japanese]

Article type: Cover
2010 Volume 20 Issue 2 Pages Cover1-
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_Cover1

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[title in Japanese]

Article type: Cover
2010 Volume 20 Issue 2 Pages Cover2-
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_Cover2

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[title in Japanese]

Article type: Appendix
2010 Volume 20 Issue 2 Pages App1-
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_App1

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[title in Japanese]

[in Japanese]

Article type: Article
2010 Volume 20 Issue 2 Pages i-
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_i

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Modified Sinc-collocation methods for integral equations of the second kind and their theoretical analysis(Theory)

Tomoaki Okayama, Takayasu Matsuo, Masaaki Sugihara

Article type: Article
2010 Volume 20 Issue 2 Pages 71-113
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_71

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In this paper the Sinc-collocation methods for integral equations of the second kind proposed by Rashidinia and Zarebnia in 2005 and 2007 are improved in the following two senses. 1) The Rashidinia-Zarebnia scheme is modified so that it can be implemented under more practical conditions. Then its convergence is proved in a rigorous manner. 2) A new scheme is developed by replacing the single exponential transformation in the Rashidinia-Zarebnia scheme with the double exponential transformation. Then it is shown both numerically and theoretically that the new scheme is far more accurate than the (modified) Rashidinia-Zarebnia scheme.

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An Approach to the Correction Equation in the Jacobi-Davidson Method : Based on a Shift Invariance Property of the Krylov Subspace on a Projected Space(Theory)

Takafumi Miyata, Tomohiro Sogabe, Shao-Liang Zhang

Article type: Article
2010 Volume 20 Issue 2 Pages 115-129
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_115

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The Jacobi-Davidson (JD) iteration method was recently proposed to compute a few eigenpairs of a large-scale and sparse matrix. In the JD method, the correction equation is solved approximately to generate the basis of a subspace for the iterative computation of eigenpairs. It is empirically known that the speed of the convergence of the JD method depends on the method for solving the correction equation. In this paper, we show a shift invariance property of the Krylov subspace on a projected space and propose a new method based on the property for solving the correction equation.

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A Note on the Effect of Some Preconditionings for the Gauss-Seidel Iterative Method

Toshiyuki Kohno, Toshihiro Nitta, Hiroshi Niki

Article type: Article
2010 Volume 20 Issue 2 Pages 131-145
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_131

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In order to improve the convergence rate of the classical iterative method, some preconditioners have been proposed. Since these preconditioners are constructed from the elements of the upper triangular parts of the coefficient matrix, the preconditioned effect is not observed on the last row of the coefficient matrix. For obtaining the preconditioning effect on the last row, Morimoto et al. proposed the nth preconditioner (n is the order of the coefficient matrix). In this note, we propose a three step preconditioner, which has an extremely small spectral radius in some examples.

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Enhancement of Convergence Stability of BiCGStab(s,L) Method

Yusuke Onoue, Seiji Fujino

Article type: Article
2010 Volume 20 Issue 2 Pages 147-163
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_147

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Sonneveld and van Gijzen brought IDR(s) method renewed from IDR method in 2008. In addition, Bi_IDR(s) method which was proposed by them is more elegant and stable than IDR(s) method. Furthermore, in 2009, BiCGStab(s,L) method was proposed as one of the generalized version of IDR(s) method with polynomial of high degree L by Tanio and Sugihara. However, convergence stability of BiCGStab(s,L) method deteriorates when parameter s is large. Therefore, we propose an enhanced version of convergence stability of BiCGStab(s,L) method. Our numerical experiments illustrates the effectiveness of enhanced BiCGStab(s,L) method.

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[title in Japanese]

Article type: Appendix
2010 Volume 20 Issue 2 Pages App2-
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_App2

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[title in Japanese]

Article type: Appendix
2010 Volume 20 Issue 2 Pages App3-
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_App3

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[title in Japanese]

Article type: Appendix
2010 Volume 20 Issue 2 Pages App4-
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_App4

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[title in Japanese]

Article type: Cover
2010 Volume 20 Issue 2 Pages Cover3-
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_Cover3

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[title in Japanese]

Article type: Cover
2010 Volume 20 Issue 2 Pages Cover4-
Published: June 25, 2010
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.20.2_Cover4

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