Transactions of the Japan Society for Industrial and Applied Mathematics

[title in Japanese]

Article type: Cover
2005 Volume 15 Issue 3 Pages Cover1-
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_Cover1

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[title in Japanese]

Article type: Cover
2005 Volume 15 Issue 3 Pages Cover2-
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_Cover2

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[title in Japanese]

Article type: Index
2005 Volume 15 Issue 3 Pages Toc1-
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_Toc1

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[title in Japanese]

Article type: Appendix
2005 Volume 15 Issue 3 Pages App1-
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_App1

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[title in Japanese]

[in Japanese]

Article type: Article
2005 Volume 15 Issue 3 Pages i-
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_i

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Precise Asymptotic Behaviour of the First Eigenvalue of Sturm-Liouville Problems with Large Drift

Masato Kimura, Shinichi Nagata

Article type: Article
2005 Volume 15 Issue 3 Pages 209-220
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_209

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This study is concerned with the asymptotic behaviour of the first eiginvalue of a Sturm-Liouville problem with a large drifting term. The magnitude of the drift is controled by a parameter p. Under a suitable condition, it is known that the first eigenvalue λ(p)>0 tends to zero exponentially if p→∞. We prove a precise behaviour of such exponential smalless of λ(p) under a relaxed condition for the drift term.

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A Cubic Interpolating Curve Assured Accuracy

Masaharu ISHII

Article type: Article
2005 Volume 15 Issue 3 Pages 221-234
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_221

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We present a new type of interpolating cubic-polynomial-curve connecting given two points with slopes given at these points. The curves are obtained by an extension of Ferguson's curves under a certain constraint. It is assured that the curves are contained within a given tolerance from the straight line connecting the two points. Conventional interpolating-curves cannot have this property. Further the curves are monotonic in the meaning of minimizing the number of inflection points, and having no singular points and no self-crossings. We show a mathematical framework to assure of this accuracy and monotony, and present an algorism to compute the curves.

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On the adaptive preconditioned iterative method

Toshiyuki Kohno

Article type: Article
2005 Volume 15 Issue 3 Pages 235-243
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_235

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We propose a new preconditioning algorithm for the Gauss-Seidel iterative method for solving a large sparse linear system Ax=b. In numerical example, we combine the preconditioned Gauss-Seidel iterative method as a preconditioner and ICCG method as a solver.

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Spline functions and n-periodic points(Wavelet Analysis, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Tsuyoshi Yoneda

Article type: Article
2005 Volume 15 Issue 3 Pages 245-252
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_245

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An operator defined by the composition of the convolution with a cardinal B-spline function and the dilation is introduced and its properties are given. By those properties, it can be applied to construct solutions of functional-differential equations and simultaneous functional-differential equations.

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Numerical Verification for Each Eigenvalues of Symmetric Matrix(Quality of Computations, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Shinya Miyajima, Takeshi Ogita, Shinichi Oishi

Article type: Article
2005 Volume 15 Issue 3 Pages 253-268
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_253

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A fast verification method of calculating guaranteed error bounds for all approximate eigenvalues of a real symmetric matrix is proposed. In the proposed algorithm, Rump's and Wilkinson's bounds are combined. By introducing Wilkinson's bound, it is possible to improve the error bound obtained by the verification algorithm based on Rump's bound with a negligible additional cost. Finally this paper includes some numerical examples to show the efficiency of the proposed method.

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Numerical Verification Method for Arbitrarily Ill-conditioned Linear Systems(Quality of Computations, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Takahisa Ohta, Takeshi Ogita, Siegfried M. Rump, Shinichi Oishi

Article type: Article
2005 Volume 15 Issue 3 Pages 269-286
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_269

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This paper is concerned with the problem of verifying an accuracy of a numerical solution of a linear system with an arbitrarily ill-conditioned coefficient matrix. In this paper, a method of obtaining an accurate numerical solution of such a linear system and its verified error bound is proposed. The proposed method is based on the accurate computation of dot product and IEEE standard 754 arithmetic. A verified and accurate numerical solution with a desired tolerance can be obtained by the proposed method with iterative refinement. Numerical results are presented for illustrating the effectiveness of the proposed method.

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On Basic Properties of The dLV Algorithm for Computing Singular Values(Applied Integrable Systems, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Masashi Iwasaki, Yoshimasa Nakamura

Article type: Article
2005 Volume 15 Issue 3 Pages 287-306
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_287

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Basic propeties of the discrete Lotka-Volterra (dLV) algorithm for computing singular values of bidiagonal matrices are considered. A relative error bound of singular values computed by the dLV algorithm is estimated. The bound is rather smaller than that of the Demmel-Kahan QR algorithm and is in the same level as the qd algorithms. Forward stability and backward stability of the dLV algorithm are also proved. Numerical examples show that the dLV algorithm has a higher relative accuracy. The modified dLV algorithm with shift (mdLVs) algorithm is shown to have quadratic or cubic convergence rate.

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Symbolic computations of the solution of simultaneous equation, the determinant and the eigen polynomial of a large scaled sparse matrix in terms of the discrete Toda equation(Applied Integrable Systems, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Kinji Kimura, Masayuki Noro, Satoshi Tsujimoto, Yoshimasa Nakamura

Article type: Article
2005 Volume 15 Issue 3 Pages 307-322
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_307

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A new method for constructing the minimum polynomial for the symbolic computation in terms of the discrete Toda equation is proposed. For the sparse matrices, the proposed method is efficiently carried out on a finite field arithmetic avoiding the division by zero. As a consequence, this paper presents new methods for the symbolic computation of the solution of simultaneous equation, the determinant and the eigen polynomial of a large scaled sparse matrix.

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Stochastic optimal velocity model and its long-lived metastable states(Applied Integrable Systems, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Masahiro Kanai, Katsuhiro Nishinari, Tetsuji Tokihiro

Article type: Article
2005 Volume 15 Issue 3 Pages 323-333
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_323

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A stochastic optimal velocity model is proposed and studied in detail. It includes the zero range process and the asymmetric simple exclusion process in special cases. The two stochastic processes are both known to be exactly solvable. The flux-density diagram shows a metastability around the intermediate density during the transition from the free state to the jamming state. It is found that the duration of the intermediate state is surprisingly long even under stochastically perturbed conditions. Moreover, the breakdown of the state into the steady jamming state happens suddenly and hence leads to a discontinuous change in the flux.

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An Analytical Approximation Formula for an American Interest Rate Option(Mathematical Finance, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Nobuo Maeda

Article type: Article
2005 Volume 15 Issue 3 Pages 335-345
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_335

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A closed form approximation formula is derived for American coupon bond options on the basis of the Geske-Johnson method under the assumption that the interest rate follows the rational log-normal model. Its strike-time discretization errors are estimated, and are found to be permissible as a rule, though they are larger than in the case of American stock options. The Geske-Johnson method would be available for estimating American interest rate options as well as for American stock options.

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Validated Computation for Bessel functions with Multiple-Precision Arithmetic(Scientific Computation and Numerical Analysis; Basics and Applications of Multiprecision Scientific Computation, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Nobito Yamamoto, Nozomu Matsuda

Article type: Article
2005 Volume 15 Issue 3 Pages 347-359
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_347

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Both multiple-precision arithmetic and validated computation have close relationship with the quality of computation. They improve and insure the quality, respectively. We propose a method to compute Bessel functions with guaranteed accuracy, which works on MATLAB. Using multiple-precision arithmetic, the method gives as precise results as one wants together with information of how precise the results are. When it is sufficient to get the results in double-precision, one can use a fast version.

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A Fundamental Solution Method with Multiple-precision Computation Applied to Reduced Wave Neumann Problems in the Exterior Region of a Disc(Scientific Computation and Numerical Analysis; Basics and Applications of Multiprecision Scientific Computation, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Fumihiro Chiba, Teruo Ushijima

Article type: Article
2005 Volume 15 Issue 3 Pages 361-384
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_361

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This paper concerns a fundamental solution method applied to Neumann boundary value problems of two dimensional reduced wave equations in the exterior region of a disc. A criterion for the unique solvability of the derived approximate problems and an error estimation for their solutions are obtained. The obtained decay rate of error is asymptotically exponential. Some results of our numerical experiments are also reported, which support the effectiveness of multiple-precision computation applied to our schemes.

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VLSI Design of FFT Multi-digit Multiplier(Scientific Computation and Numerical Analysis; Basics and Applications of Multiprecision Scientific Computation, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Syunji Yazaki, Koki Abe

Article type: Article
2005 Volume 15 Issue 3 Pages 385-401
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_385

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We designed a VLSI (Very Large Scale Integrated circuit) chip of FFT multiplier using a floating-point representation with optimal data length based on an experimental error analysis. Using the hardware implementation, we can perform 2^5 to 2^<13> hexadecimal digit (39 to 9,831 decimal digit) multiplication 25.1 to 45.6 times (33.9 times in average) faster than using FFTW3, at an area cost of 9.05mm^2. The hardware FFT multiplier has 64 times faster performance than exflib (a multi-digit arithmetic library using Karatsuba method) for longer than 2^<21> hexadecimal digit (≒2,520,000 decimal digit) multiplication. Considering the wide applications of its FFT modules, the performance and cost of the FFT multiplier justifies the VLSI implementation.

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New Multiple-Precision Arithmetic Environment and Its Application to Numerical Computations(Scientific Computation and Numerical Analysis; Basics and Applications of Multiprecision Scientific Computation, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Hiroshi FUJIWARA, Yuusuke ISO

Article type: Article
2005 Volume 15 Issue 3 Pages 403-417
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_403

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We propose a multiple-precision arithmetic environment, which reduces influence of rounding errors, as a clue of qualitative improvement of scientific computations. The usual double precision system is not satisfactory for computations of numerically unstable problems although it has about 15 digits accuracy in representation and computation of real numbers, but our proposed environment gives a new method to deal with them and enable us to carry out high accurate computations. We show the effective use of multiple-precision arithmetic for numerical treatments of analytic functions and high-accurate numerical integration formula. Such ultimate accuracy is necessary in numerical computations of inverse and ill-posed problems. Proposed environment is designed for new 64-bit personal computer architectures.

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High-precision numerical computation of integral equations of the first kind(Scientific Computation and Numerical Analysis; Basics and Applications of Multiprecision Scientific Computation, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Hiroshi FUJIWARA, Hitoshi IMAI, Toshiki TAKEUCHI, Yuusuke ISO

Article type: Article
2005 Volume 15 Issue 3 Pages 419-434
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_419

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A new method for the direct numerical computation of integral equations of the first kind, of which the integral kernels are analytic, is proposed. The basic idea of the method is based on combination of the spectral collocation method and the multiple precision computation. It gives good numerical results for the equations as far as we don't admit observation errors in the given inhomogeneous terms, and the results implies possibility of numerical analytic continuation on the multiple precision arithmetic. A new accurate rule for numerical integration is also introduced.

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Effectiveness of the Multi-precision Arithmetic on Inverse Heat Conduction Problems(Scientific Computation and Numerical Analysis; Basics and Applications of Multiprecision Scientific Computation, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Kentaro Iijima, Kazuei Onishi

Article type: Article
2005 Volume 15 Issue 3 Pages 435-443
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_435

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We show a numerical method for the Cauchy problem of the Laplace equation and the backward heat conduction problem with ill-posedness. The numerical method consists of the multi-precision arithmetic and a high order finite difference method in which sampling points can be arbitrarily located in the domain of the problem. It is our strategy to suppress the influence on the accuracy of the numerical solution from the rounding error and the discretization error because of the instability of the solution. In numerical examples, we can obtain the numerical solution with high accuracy of the ill-posed problems.

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An Extension of the Conjugate Residual Method for Solving Nonsymmetric Linear Systems(Algorithms for Matrix・Eigenvalue Problems and their Applications, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Tomohiro SOGABE, Masaaki SUGIHARA, Shao Liang ZHANG

Article type: Article
2005 Volume 15 Issue 3 Pages 445-459
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_445

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The Conjugate Gradient (CG) method and the Conjugate Residual (CR) method are well-known Krylov subspace methods for solving symmetric (positive definite) linear systems. For solving nonsymmetric ones, Fletcher extended the CG method to nonsymmetric linear systems. The resulting method is also well known as the Bi-CG method. The purpose of this paper is to extend the CR method to nonsymmetric linear systems. Numerical experiments show that the resulting method, named Bi-Conjugate Residual (Bi-CR), is often more efficient than the Bi-CG method.

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Accurate Twisted Factorization of Real Symmetric Tridiagonal Matrices and Its Application to Singular Value Decomposition(Algorithms for Matrix・Eigenvalue Problems and their Applications, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Masashi Iwasaki, Shinya Sakano, Yoshimasa Nakamura

Article type: Article
2005 Volume 15 Issue 3 Pages 461-481
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_461

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A new algorithm for an accurate twisted factorization of real symmetric tridiagonal matrices is presented. Two transformations derived from certain discrete Lotka-Volterra (dLV) systems play a key role. The algorithm is shown to be useful to compute singular vectors of upper bidiagonal matrices. Combining it with the mdLVs algorithm for accurate singular values, a new singular value decomposition (SVD) algorithm named integrable SVD (I-SVD) algorithm is designed. It is shown that I-SVD runs much faster than a credible SVD routine DBDSQR with the same accuracy at least in three different types of test matrices.

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An error analysis of a direct reconstruction method for the EEG inverse source problem(Algorithms for Matrix・Eigenvalue Problems and their Applications, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Junji Oohama, Tetsuya Sakurai, Takaaki Nara

Article type: Article
2005 Volume 15 Issue 3 Pages 483-494
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_483

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In this paper, we present an error analysis of a direct reconstruction method for the EEG inverse source problem. Using the Green formula and weighting harmonic functions, the inverse source problem is reduced to a generalized eigenvalue problem. We analyze the stability of the generalized eigenvalue problem and show that the accuracy of the solution can be evaluated by the noise level, the source positions and intensities.

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The Accuracy Improvement of Numerical Conformal Mapping using Pade Approximation by Arnoldi method(Algorithms for Matrix・Eigenvalue Problems and their Applications, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Yi Bin LU, Taku ITOH, Shoji ITOH, Tetsuya SAKURAI

Article type: Article
2005 Volume 15 Issue 3 Pages 495-508
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_495

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In this paper, we consider a method for computation of numerical conformal mappings using Pade approximation. This method calculates the poles of the denominator of a Pade approximation as charge points, using the results obtained by the charge simulation method proposed by Amano et al. Although good accuracy of numerical conformal mapping can be obtained using a few charge points, the accuracy is degraded when a certain number of charge points is exceeded. In order to improve the accuracy of this method, we reduce calculations of charge points by Pade approximation to a generalized eigenvalue problem. Moreover, we construct a highly accurate unitary matrix to appear in this generalized eigenvalue problem using the Arnoldi method. Some numerical examples illustrate the efficiency of the improved method.

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[title in Japanese]

Article type: Appendix
2005 Volume 15 Issue 3 Pages App2-
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_App2

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[title in Japanese]

Article type: Appendix
2005 Volume 15 Issue 3 Pages App3-
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_App3

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[title in Japanese]

Article type: Appendix
2005 Volume 15 Issue 3 Pages App4-
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_App4

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[title in Japanese]

Article type: Index
2005 Volume 15 Issue 3 Pages Toc2-
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_Toc2

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[title in Japanese]

Article type: Cover
2005 Volume 15 Issue 3 Pages Cover3-
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_Cover3

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[title in Japanese]

Article type: Cover
2005 Volume 15 Issue 3 Pages Cover4-
Published: September 25, 2005
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/jsiamt.15.3_Cover4

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