Transactions of the Japan Society for Industrial and Applied Mathematics

[title in Japanese]

Article type: Cover
2006 Volume 16 Issue 4 Pages Cover1-
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_Cover1

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[title in Japanese]

Article type: Cover
2006 Volume 16 Issue 4 Pages Cover2-
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_Cover2

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[title in Japanese]

Article type: Index
2006 Volume 16 Issue 4 Pages Toc1-
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_Toc1

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[title in Japanese]

Article type: Appendix
2006 Volume 16 Issue 4 Pages App1-
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_App1

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[title in Japanese]

[in Japanese]

Article type: Article
2006 Volume 16 Issue 4 Pages A1-
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_A1

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[title in Japanese]

Article type: Appendix
2006 Volume 16 Issue 4 Pages App2-
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_App2

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Ostwald ripening in a thin liquid film(Application)

Hidenori Yasuda, Masaaki Matsumoto

Article type: Article
2006 Volume 16 Issue 4 Pages 359-370
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_359

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We study phenomena called Ostwald ripening in a thin liquid film by a numerical method. Droplets such as oil-water system in a thin film disappear or grow slowly. We simulate these phenomena by the invariant finite difference scheme of the two-phase shallow water equations. We show that difference of chemical potential between surface of droplets and outside of droplets plays an important role, and we also evaluate the speed of the flow outside droplets by the reductive perturbation method.

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A New Stochastic Cellular Automaton Model on Traffic Flow and Jamming Phase Transition(Application)

Satoshi Sakai, Katsuhiro Nishinari, Shinji Iida

Article type: Article
2006 Volume 16 Issue 4 Pages 371-384
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_371

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This paper presents a stochastic extension of a traffic cellular automatom (CA) model with slow-to-start effect and a driver's perspective. This new model includes, as special cases, previously known traffic CA models such as Nagel-Schreckenberg model, Quick-Start model, and Slow-Start model. Fundamental diagrams and phase diagrams are numerically calculated. It is shown that metastables states in fundamental diagrams do not disappear even when stochastic effect is present, i.e., the metastable states are stable against perturbations. The combination of fundamental diagrams and approximate flow-density relations at boundaries successfully gives analytic expressions of phase transiton lines which almost coincides with those obtained from numerical simulations.

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A Variant of the ORTHOMIN(m) Method and its Application to Singular Linear Systems

Kuniyoshi ABE, Shao-Liang ZHANG

Article type: Article
2006 Volume 16 Issue 4 Pages 385-398
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_385

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We propose a variant of the ORTHOMIN (m) method for solving linear systems Ax=b. It is mathematically equivalent to the original ORTHOMIN (m) method, but uses recurrence formulas that are different from those of ORTHOMIN (m); they contain alternative expressions for the auxiliary vectors and the recurrence coefficients. Also, our proposed algorithm has the same computational costs as ORTHOMIN (m). Through numerical experiments on nonsingular linear systems we confirm the equivalence on numerical computations with finite precision arithmetic, and numerical experiments on singular linear systems show that our proposed algorithm is more accurate and less affected by rounding errors than the original.

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Deflated CG method for solving the trapezoidal rule

Shinsuke Nakamura, Taketomo Mitsui

Article type: Article
2006 Volume 16 Issue 4 Pages 399-420
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_399

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We are concerned with an efficient numerical solution of linear equations at each time-stepping of the trapezoidal rule applied to a system of ordinary differential equations (ODEs), which is assumed to be linear with a constant coefficient matrix of large dimension. By referring to the idea of the deflated CG method by Y. Saad et al, the present paper describes a method to share several computational costs in the CG process over a number of computational steps. It can suppress increase of the memory usage as well as reduce the total number of CG iteration. Numerical examples depict its efficiency.

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Totally Conservative Integrator and Its Symmetrization for Integrable Relativistic Equation of Motion(Applied Integrable System,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Tetsu R. Satoh

Article type: Article
2006 Volume 16 Issue 4 Pages 421-433
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_421

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This paper presents numerical solutions for relativistic dynamics by the Symplectic Integrator (SI) and Totally Conservative Integrator (TCI), and proposes Symmetric TCI (S-TCI) for improving the TCI. For some kinetic problems, the TCI is more efficient than the SI, e.g. faster calculation and higher accuracy. However, some inaccuracy results by the TCI for relativistic dynamics are indicated. To overcome its problem, time-reversal S-TCI is derived based on composition methods with the adjoint method. Numerical solutions by S-TCI show greatly improvement compared with the ordinary TCI.

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Numerical Algorithm using Compartment Model Analysis for Estimating Permeability in Renal Tissue(Practice,Scientific Computation and Numerical Analysis,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Youhei Nanazawa, Hiroshi Suito, Takuya Ueda, Manabu Minami

Article type: Article
2006 Volume 16 Issue 4 Pages 435-452
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_435

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Permeability is valuable information for tumor-tissue diagnosis. In this study, permeability is estimated using Compartment Model Analysis from the concentration of contrast media obtained by computed tomography examination of renal cell cancer. The expression for concentration of the contrast media obtained using the Compartment Model Analysis is a first-order linear ordinary differential equation. Permeability is determined by minimizing the difference between values obtained from measurements and values obtained as the solution of the expression. The Broyden-Fletcher-Golefarb-Shanno quasi-Newton method and a genetic algorithm with distance-independent diversity control are used for minimization.

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An Improvement of Multiple Division Divide-and-Conquer for Real Symmetric Tridiagonal Eigenproblem(Theory,Algorithms for Matrix/Eigenvalue Problems and their Application,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Yutaka Kuwajima, Takaomi Shigehara

Article type: Article
2006 Volume 16 Issue 4 Pages 453-480
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_453

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We improve divide-and-conquer with multiple divisions for real symmetric tridiagonal eigenproblem proposed in [13]. The main improvements are the following two. The first is that we succeed in developing an algorithm for keeping the orthogonality among eigenvectors in double-precision floating-point number processing without a substantial increase of numerical cost. As a result, all the calculations are done without quadruple-precision floating-point number processing, which is required in [13]. The second is that we implement a deflation effect which substantially decreases numerical cost. As a result of these two improvements, we succeed in developing a program for real symmetric tridiagonal eigenproblem which is even faster than a LAPACK routine DSTEVD, while keeping a numerical accuracy comparable to DSTEVD.

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Performance evaluation of diagonal-compensated ILUC decomposition preconditioner(Algorithms for Matrix/Eigenvalue Problems and their Application,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Maki FUJIWARA, Seiji FUJINO

Article type: Article
2006 Volume 16 Issue 4 Pages 481-496
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_481

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The Grout variant of ILU preconditioner developed recently is an attractive and effective preconditioner over the conventional row-based ILU preconditioned This paper explores dropping strategy for fill-in to improve the robustness of ILUC. This paper shows how to compensate a diagonal entry of matrix influenced by dropping. The performances of diagonal-compensated ILUC preconditioner are compared with the ILUT, ILUC decomposition on a set of problems. Results of numerical experiments show that diagonal-compensated ILUC preconditioner outperforms well.

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On an evaluation method of preconditioners for complex symmetric systems of linear equations(Algorithms for Matrix/Eigenvalue Problems and their Application,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Masayuki OKADA, Hiroto TADANO, Tetsuya SAKURAI

Article type: Article
2006 Volume 16 Issue 4 Pages 497-505
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_497

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As preconditioners for complex symmetric systems of linear equations, incomplete Cholesky decomposition and complex shifted incomplete Cholesky decomposition are well-known. These preconditioners have two parameters, threshold value and shift parameter. It is difficult to choose effective parameters for these preconditioners. In this paper, we evaluate preconditioning matrices by using Precise Remainder Index (PRI) in order to choose effective parameters. We investigate the relationship between the number of iterations in Krylov subspace iterative method and PRI by numerical experiments.

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Recent Developments in Algorithms for Solving Dense Eigenproblems (II) : Multishift QR Algorithms(Survey,Algorithms for Matrix/Eigenvalue Problems and their Application,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Yusaku Yamamoto

Article type: Article
2006 Volume 16 Issue 4 Pages 507-534
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_507

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The QR algorithm is one of the most reliable and widely used methods to compute the eigenvalues of symmetric and nonsymmetric matrices. However, it is not straightforward to execute the QR algorithm efficiently on modern architectures such as processors with hierarchical memory or parallel computers because of its inherent sequential nature and low data reference locality. To overcome this difficulty, Bai & Demmel proposed the multishift QR algorithm in 1989 and this idea has been greatly expanded since then. In this paper, we introduce the basic theory of the multishift QR algorithm and review recent developments to improve its efficiency, such as the two-tone QR algorithm, aggressive early deflation and the fully-pipelined multishift QR algorithm. Directions for future research are also discussed.

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Numerical Verification for Each Eigenpair of Symmetric Matrix(Theory,Quality of Computation,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Shinya Miyajima, Takeshi Ogita, Shin'ichi Oishi

Article type: Article
2006 Volume 16 Issue 4 Pages 535-552
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_535

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A fast method for enclosing each eigenpairs of real symmetric matrix is proposed. First, error bounds of all approximate eigenvectors are proposed. The proposed method is constructed by combining these bounds and the fast method for enclosing each eigenvalue previously developed by the authors. Utilizing intermediate results in the previous method, computational cost for enclosing each eigenvector become almost negligible. Numerical results are presented showing the efficiency of the proposed method. As an application of the proposed method, an efficient method of bounding each pair of singular value and singular vector of a real matrix is sketched.

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Fast and Robust Algorithm for Geometric Predicates using Floating-Point Arithmetic(Practice,Quality of Computation,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Katsuhisa Ozaki, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oish ...

Article type: Article
2006 Volume 16 Issue 4 Pages 553-562
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_553

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This paper is concerned with the computational geometry. A number of geometric problems can be boiled down to the determinant predicates, i.e. whether the sign of the determinant is positive, negative or zero. Among such problems, the ORIENT3D is focused in this paper. A fast and adaptive method for rigorously solving ORIENT3D is proposed. The proposed method in this paper is based on a new accurate floating-point summation algorithm which has just been developed by Rump, Ogita and Oishi. The proposed method ideally works with depending on difficulty of the problem, i.e., if the condition number of the problem becomes larger, then the computational cost for the method gradually increases. Numerical results are presented for illustrating that the proposed method is faster than the state-of-the-art method proposed by Demmel-Hida.

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Estimating the Downsian locations of parties from the numbers of votes gained by the parties : We can use the normal as the voters' distribution(Application,Mathematical Politic,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Takahiro Kubo, Mitsuyo Yamamoto, Kazuo Kishimoto

Article type: Article
2006 Volume 16 Issue 4 Pages 563-574
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_563

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Following the approach by Kishimoto et al. [4], this paper calculates the Downsian political locations of major four parties in the Japanese national elections from the numbers of votes gained by the parties, assuming that the voters' distributions at districts are t distributions (d.f=3,4,...,50). Since the results are similar to those in the case of normal density, we can use the normal density as the voters' distribution at the districts.

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The Increase of "No Party Support" Group as Post Cold War Process(Application,Mathematical Politic,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Tomoyuki Ide

Article type: Article
2006 Volume 16 Issue 4 Pages 575-589
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_575

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We can predict the industrialization of our country will cause some decrease in the number of the reformist and contrastively some increase in the number of the conservative. But the trend of the conservative has stayed the same or decreased in number. Simultaneously, the number of the voter who supports no party has been increased. The purpose of this paper is proposing a schema to explain these tendencies on the whole. It seems reasonable to conclude the voter who leaves the reformists join in the conservatives, and the voter who leaves conservatives join in the voters who support no party.

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A High-Density Knapsack Cryptosystem Using Combined Trapdoor(Application,Algorithmic Number Theory and Its Application,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Takeshi Nasako, Yasuyuki Murakami

Article type: Article
2006 Volume 16 Issue 4 Pages 591-605
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_591

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Merkle and Hellman proposed a knapsack scheme using the superincreasing sequence as a trapdoor. Kasahara and Murakami introduced the trapdoor using even-odd check in shifted values of the secret sequence. These sequences are typical trapdoors of knapsack schemes using the modular multiplication. In this paper, we propose a method of combining these trapdoors. We also propose a high-density knapsack cryptosystem using the proposed trapdoor. Moreover, we discuss on the security of the proposed scheme against Shamir's attack and the low-density attack which are conventional attacks for knapsack schemes.

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Mathematical Modeling of Stable Quasi-Static Crack Extension by Extended Griffith Energy Balance Theory(Theory,Continuum Mechanics Focusing Singularitie,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Kohji Ohtsuka

Article type: Article
2006 Volume 16 Issue 4 Pages 607-630
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_607

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Griffith's approach to fracture mechanics is very powerful, and there are many extensions and modifications of Griffith's work. We observe stable crack extension before fracture; for example, cracking occurs under repeated loading (fatigue failure). However, Griffith's approach is so that it is applicable only under constant loading. In this paper, first, Griffith's theory is modified available under varying loads. With this modification, Griffith's energy balance theory is extended in consideration of second expansion of energies and crack extension resistance with respect to time, which shows importance of varying load in stable crack extension. The research is done in 3-dimensional cases in wide class.

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Smooth and Safety Path Planning for Car-like Robot in Region with Polygonal Obstacles(Application,Discrete System,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

Yusuke Matsumoto, Ippei Suzuki, Keiko Imai

Article type: Article
2006 Volume 16 Issue 4 Pages 631-649
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_631

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In this paper, we consider a path planning problem for a car-like robot with nonholonomic constraints in motion planning. The path should be smooth and the steering angle has to change continuously. Various techniques have been proposed. However, those methods vary the angular velocity or they do not give a consideration to obstacles in the work space. We propose a new method of finding a path by the Voronoi graph and the clothoid curve which has uniform angular velocity. By using the obtained path, the robot can move smoothly and avoid collision with the obstacles as far as possible.

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[title in Japanese]

Article type: Index
2006 Volume 16 Issue 4 Pages 293-295
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_293

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[title in Japanese]

Article type: Index
2006 Volume 16 Issue 4 Pages 296-300
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_296

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[title in Japanese]

Article type: Appendix
2006 Volume 16 Issue 4 Pages App3-
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_App3

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[title in Japanese]

Article type: Appendix
2006 Volume 16 Issue 4 Pages App4-
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_App4

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[title in Japanese]

Article type: Appendix
2006 Volume 16 Issue 4 Pages App5-
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_App5

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[title in Japanese]

Article type: Index
2006 Volume 16 Issue 4 Pages Toc2-
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_Toc2

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[title in Japanese]

Article type: Cover
2006 Volume 16 Issue 4 Pages Cover3-
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_Cover3

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[title in Japanese]

Article type: Cover
2006 Volume 16 Issue 4 Pages Cover4-
Published: December 25, 2006
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.16.4_Cover4

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