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 4

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[title in Japanese]

Article type: Cover
2007 Volume 17 Issue 4 Pages Cover1-
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_Cover1

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[title in Japanese]

Article type: Cover
2007 Volume 17 Issue 4 Pages Cover2-
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_Cover2

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[title in Japanese]

Article type: Index
2007 Volume 17 Issue 4 Pages Toc1-
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_Toc1

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[title in Japanese]

Article type: Appendix
2007 Volume 17 Issue 4 Pages App1-
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_App1

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[title in Japanese]

[in Japanese]

Article type: Article
2007 Volume 17 Issue 4 Pages i-
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_i

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[title in Japanese]

Article type: Appendix
2007 Volume 17 Issue 4 Pages App2-
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_App2

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Generating 4-connected plane triangulations(Theory)

Hironori Takano, Shin-ichi Nakano

Article type: Article
2007 Volume 17 Issue 4 Pages 363-397
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_363

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A "based" plane triangulation is a plane triangulation with one designated edge on the outer face. In this paper we give a simple algorithm to generate all 4-connected based plane triangulations with at most n vertices. This is the first algorithm to generate such triangulations. The algorithm uses O(n) space and generates such triangulations in O(n) time per triangulation without duplications. By modifying the algorithm one can generate all 4-connected (non-based) plane triangulations with at most n vertices in O(n^2) time per triangulation without duplications.

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An Experiment of the Orthonormalization Method with Higher Locality of Memory References for a Large Matrix of Very Slim-Shape(Application)

Hiroshi Murakami

Article type: Article
2007 Volume 17 Issue 4 Pages 399-454
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_399

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For the orthonormalization of a large matrix of very slim-shape, compared from the ordinal method such as the modified Gram-Schmidt or the Householder-QR, the classical singular value decomposition method (CSVD) with orthonormality corrections has the higher locality of memory references which reduces the amount of data transfer across the storage hierarchy between the cache and the main memory or between the main memory and the external storage device, which makes the fast computation possible. From experiments on several computer systems, in certain cases the CSVD method can be several times faster than the modified Gram-Schmidt is examined.

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Difference equations with an invariant expressed in terms of the hypergeometric function(Theory, Applied Integrable System, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Takeshi Sakaki, Saburo Kakei

Article type: Article
2007 Volume 17 Issue 4 Pages 455-462
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_455

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We introduce a method for constructing difference equations with an invariant expressed as hypergeometric functions. Examples including the equations associated with the arithmetic-geometric mean and the arithmetic-harmonic mean are given.

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Discrete stochastic processes and q-hypergeometric functions(Theory, Applied Integrable System, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Takeshi Ga, Saburo Kakei, Yasushi Kitane

Article type: Article
2007 Volume 17 Issue 4 Pages 463-468
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_463

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We propose an discrete analogue of the Feynman-Kac formula based on an asymmetric random walk. We investigate a class of solutions for the partial difference equaion in the discrete the Feynman-Kac formula.

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Construction of variant Hermite elements of degree 3 for the Dirichlet boundary conditions(Theory, Scientific Computation and Numerical Analysis, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Yuki Ueda, Masahisa Tabata

Article type: Article
2007 Volume 17 Issue 4 Pages 469-479
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_469

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The Hermite triangular element of degree three requires partial derivative values at the degrees of freedom. It can reconstruct polynomials of degree three on each element. In the case of problems subject to Dirichlet boundary conditions partial derivative values are not given on the boundary. We cannot, therefore, apply the element directly to those problems. Here we make variants of the Hermite element. Replacing the conventional Hermite elements by them near the boundary enables us to treat those problems easily. We apply this method to the Poisson problem to present the best possible a priori estimate and some numerical results.

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Numerical Computation on Continuation of the Solution for the One-Dimensional Heat Equation(Scientific Computation and Numerical Analysis, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Hitoshi Imai, Hideo Sakaguchi

Article type: Article
2007 Volume 17 Issue 4 Pages 481-493
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_481

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We consider a problem governed by the simple one-dimensional heat equation. In our problem two parameters are introduced. One is for the determination of the initial boundary value problem, the continuation problem or the initial value problem. Another one is for analiticity. Numerical simulations are carried out by using two different numerical methods(FDM⊕EE and IPNS). Numerical results are interesting as follows: Both methods give similar results converging to the smooth solution for the initial value problem which has non-uniqueness of the solution. Moreover, both methods give different results for the continuation problem.

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A proposal of Modified S(Stabilized) CRS method based on residual vector of BiCR method(Algorithms for Matrix/Eigenvalue Problems and their Applications, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Yusuke Onoue, Seiji Fujino, Kuniyoshi Abe

Article type: Article
2007 Volume 17 Issue 4 Pages 495-509
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_495

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It is known that SCGS method has stability of convergence as compared with the conventional CGS method. However, the amount of computational costs per single iteration of the SCGS method is fairly increased. On the other hand, product type of BiCR iterative method whose residual vector is based on that of the original BiCR method was recently proposed. In this paper, we propose two types of the CRS method, i.e., S(Stabilized) CRS and M(Modified) SCRS methods. Through numerical experiments, we verify stability of convergence and efficiency of these iterative methods.

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A Method for Estimating a Distribution of Eigenvalues using the AMLS Method(Algorithms for Matrix/Eigenvalue Problems and their Applications, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Kenta SENZAKI, Hiroto TADANO, Tetsuya SAKURAI

Article type: Article
2007 Volume 17 Issue 4 Pages 511-521
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_511

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We propose an efficient method for estimating the distribution of eigenvalues using the AMLS method. We combine the AMLS method and the CIRR method. AMLS calculates approximate eigenpairs fast and has been shown to be efficient for vibration and acoustic analysis. However, the application areas of this method have been limited because its accuracy is usually less than that of other methods. We show that the proposed method is effective at the result of applying this method to the molecular orbital calculations.

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An Efficient Implicit Wavelet Sparse Approximate Inverse Preconditioner Using Blocked Finger Pattern(Algorithms for Matrix/Eigenvalue Problems and their Applications, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Akira Imakura, Tomohiro Sogabe, Shao-Liang Zhang

Article type: Article
2007 Volume 17 Issue 4 Pages 523-542
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_523

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Recently, the implicit wavelet sparse approximate inverse (IW-SPAI) preconditioner has been proposed for large and sparse nonsymmetric linear systems. The preconditioning matrix has a certain sparse structure called finger pattern and it can be obtained by the solutions of some least squares problems. By reusing the result of QR factorization in some least squares problems, in order to improve the performance of the IW-SPAI, in this paper, an IW-SPAI using Blocked finger pattern (BIW-SPAI) is proposed as a variant of the IW-SPAI. Numerical experiments indicate that the BIW-SPAI is often more efficient than the IW-SPAI.

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Spatial Competition : A Survey(Survey, Mathematical Politics, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Kuninori Nakagawa

Article type: Article
2007 Volume 17 Issue 4 Pages 543-558
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_543

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This paper aims at providing a brief review over the literature on spatial competition a la Hotelling and its major extensions. We also explore an economic implication embedded in its mathematical structure. In section 1, we survey the Hotelling spatial competition and its major extensions. In section 2, we discuss its mathematical structure, focusing mainly on consumer preferences and those distributions.

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Partial Knowledge of Functions and Verification of Anonymity(Theory, Formal Approach to Information Security, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Yuusuke Kawamoto, Ken Mano, Hideki Sakurada, Masami Hagiya

Article type: Article
2007 Volume 17 Issue 4 Pages 559-576
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_559

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This paper proposes a method for formalizing and analyzing a partial knowledge of cryptographic functions within the runs and systems framework of multi-agent systems. We consider a multi-agent system where the interpretation of the cryptographic functions may vary from run to run. In this new model, we formalize the anonymity and coercion-resistance of electronic voting protocols in the presence of active adversaries, present a method for verifying these properties, and apply it to a practical electronic voting protocol. We also discuss computational justification for the method.

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An improvement on the computation of 2-power torsion points on genus 2 hyperelliptic curves(Theory, Algorithmic Number Theory and Its Applications, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Shunji Kozaki, Kazuto Matsuo

Article type: Article
2007 Volume 17 Issue 4 Pages 577-593
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_577

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Gaudry and Harley proposed a Schoof-like algorithm for genus 2 hyperelliptic curves which uses the 2-power torsion points on the Jacobians. Using actions of the 2 torsion subgroups on the 2-power torsion points, Gaudry and Schost improved the 2-power torsion point computation. This paper shows properties of the halved points of the 2-power torsion points and the actions of the 2 torsion subgroups. By using these properties, this paper improves the computation of the 2-power torsion points. Moreover, an implementation of the improved algorithm is shown in this paper. The implementation results show that the improvement is efficient.

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More constructing pairing-friendly elliptic curves for cryptography(Application, Algorithmic Number Theory and Its Applications, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Satoru Tanaka, Ken Nakamula

Article type: Article
2007 Volume 17 Issue 4 Pages 595-606
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_595

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The problem of constructing elliptic curves suitable for pairing applications has received a lot of attention. To solve this problem, we propose a variant of the Brezing and Weng method. And we produce new families of parameters for pairing-friendly elliptic curves.

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Distribution of fundamental units of real quadratic number fields(Algorithmic Number Theory and Its Applications, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Takeshi Yasue

Article type: Article
2007 Volume 17 Issue 4 Pages 607-615
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_607

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Let p be a prime number which satisfies p ≡ 1(mod 4). Let ε_p=t_p+u_p√<p>/2>1 be the fundamental unit of the real quadratic number field Q(√<p>). In this note, we study some distributions of t_p, u_p from a few viewpoints. For all computations in this paper, we used PARI/GP.

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[title in Japanese]

Article type: Index
2007 Volume 17 Issue 4 Pages A255-A257
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_A255

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[title in Japanese]

Article type: Index
2007 Volume 17 Issue 4 Pages A258-A261
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_A258

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[title in Japanese]

Article type: Appendix
2007 Volume 17 Issue 4 Pages App3-
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_App3

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[title in Japanese]

Article type: Appendix
2007 Volume 17 Issue 4 Pages App4-
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_App4

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[title in Japanese]

Article type: Appendix
2007 Volume 17 Issue 4 Pages App5-
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_App5

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[title in Japanese]

Article type: Index
2007 Volume 17 Issue 4 Pages Toc2-
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_Toc2

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[title in Japanese]

Article type: Cover
2007 Volume 17 Issue 4 Pages Cover3-
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_Cover3

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[title in Japanese]

Article type: Cover
2007 Volume 17 Issue 4 Pages Cover4-
Published: December 25, 2007
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.17.4_Cover4

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