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 4

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[title in Japanese]

Article type: Cover
1999 Volume 9 Issue 4 Pages Cover1-
Published: December 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.4_Cover1

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[title in Japanese]

Article type: Cover
1999 Volume 9 Issue 4 Pages Cover2-
Published: December 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.4_Cover2

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[title in Japanese]

Article type: Appendix
1999 Volume 9 Issue 4 Pages App1-
Published: December 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.4_App1

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[title in Japanese]

[in Japanese]

Article type: Article
1999 Volume 9 Issue 4 Pages i-
Published: December 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.4_i

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[title in Japanese]

Article type: Appendix
1999 Volume 9 Issue 4 Pages App2-
Published: December 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.4_App2

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Rational Approximation of Incomplete Gamma Function for the Sake of Effective Molecular Orbital Calculations

Takashi Amisaki, Shigeru Obara, Umpei Nagashima

Article type: Article
1999 Volume 9 Issue 4 Pages 151-163
Published: December 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.4_151

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A method has been developed for an efficient approximation of incomplete gamma function that occurs in molecular orbital calculation with Gaussian-type basis sets. The method employs rational Chebyshev approximation and forward and backward recurrence relations to reduce the memory-space requirement without compromising accuracy. An example is illustrated for the cases wherein the sum of quantum numbers of orbitals is less than or equal to 8 and the rational functions are evaluated using double-precision numbers. In sucha case, results accurate to 50 significant bits can be obtained.

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Improvement of the π Calculation Algorithm and Implementation of Fast Multiple-Precision Computation

Takuya OOURA

Article type: Article
1999 Volume 9 Issue 4 Pages 165-172
Published: December 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.4_165

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In this paper, we derive efficient quadratic and quartic iteration algorithms from the improvement of Gauss'arithmetic-geometric mean (AGM) algorithm. The number of multiplications in the improved quadratic algorithm is only half the number of the original algorithm, but the number of the square root operations in the improved AGM iterations is equal to the number of the original algorithm. So we derive an efficient simultaneous Newton iteration for the square root calculation. Next, weimplement a fast multiple-precision computation for the proposed algorithms and estimate the number of floating point operations and the execution time to compute the AGM iterations.

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[title in Japanese]

Article type: Index
1999 Volume 9 Issue 4 Pages Toc1-
Published: December 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.4_Toc1

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[title in Japanese]

Article type: Index
1999 Volume 9 Issue 4 Pages Index1-
Published: December 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.4_Index1

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[title in Japanese]

Article type: Appendix
1999 Volume 9 Issue 4 Pages App3-
Published: December 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.4_App3

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[title in Japanese]

Article type: Cover
1999 Volume 9 Issue 4 Pages Cover3-
Published: December 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.4_Cover3

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[title in Japanese]

Article type: Cover
1999 Volume 9 Issue 4 Pages Cover4-
Published: December 15, 1999
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.9.4_Cover4

JOURNAL FREE ACCESS

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