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Article type: Cover
2009 Volume 19 Issue 1 Pages
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Article type: Cover
2009 Volume 19 Issue 1 Pages
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Article type: Appendix
2009 Volume 19 Issue 1 Pages
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[in Japanese]
Article type: Article
2009 Volume 19 Issue 1 Pages
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Published: March 25, 2009
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Article type: Appendix
2009 Volume 19 Issue 1 Pages
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Shinsuke Hamada
Article type: Article
2009 Volume 19 Issue 1 Pages
1-23
Published: March 25, 2009
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We consider the blow-up problem for the generalized Proudman-Johnson equation parameterized by a∈R. By using the adaptive meshes, we numerically compute blow-up solutions of the generalized Proudman-Johnson equation, and discuss the relation between the parameter a and blow-up profile, blow-up time, and blow-up rate. We then examine the blow-up rate of the solution by using the asymptotic analysis, and show that the only possible blow-up rate is 1 if a>1 and a is not an integer.
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Kenji Tomoeda, Tatsuyuki Nakaki
Article type: Article
2009 Volume 19 Issue 1 Pages
25-37
Published: March 25, 2009
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The interaction between diffusion and absorption suggests some interesting phenomena in several fields. Numerical computation to the model equation which describes such an interaction suggests a remarkable property on the support of solution; that is, after support splitting phenomena appear, the support becomes connected, and thereafter the support splits again. In this paper we construct an initial function for which such a property appears by making use of the particular solutions. Moreover, we justify repeated numerical support splitting and connecting phenomena.
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Yohei Sato, Hiroshi Okuda
Article type: Article
2009 Volume 19 Issue 1 Pages
39-55
Published: March 25, 2009
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In the calculations of perturbations terms in SFEM, coefficient matrices are always the same. For such kind of problems, a single seed method and its derivations have been reported. The Seed Method is a kind of Krylov Subspace Methods which can reduce computational cost of CG iterations recycling the subspaces produced by one seed system. We applied the Seed Method and implemented in the framework of SFEM. Numerical examples have shown that the total time of calculations of perturbation terms has been reduced to 55%.
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Masaharu Ishii, Akinori Yoshimoto
Article type: Article
2009 Volume 19 Issue 1 Pages
57-71
Published: March 25, 2009
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By applying the structure of the group of reduced residue classes of residue ring R=Z/2^wZ, we obtain the following results. We prove that the equations of degree two can be solved in at most polynomial time and their solutions have many branches generally. We can decode Diffie-Hellman type of key exchange algorithm given by substituting of Chebyshev polynomials in at most polynomial time, in the case that the generators of the key are even numbers. Moreover we show the characteristic of quantity of computation of the map obtained by the discretized chaotic map using Chebyshev polynomials.
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Takuya OOURA
Article type: Article
2009 Volume 19 Issue 1 Pages
73-79
Published: March 25, 2009
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The double exponential formula is well-known as a powerful numerical quadrature rule, but is weak to integral transforms of a certain kind (for example, Fourier transform, Hankel transform, Bessel transform and Hilbert transform). When the double exponential formula is applied to these transforms, the number of function evaluations increases very much. In this paper, we propose a powerful and efficient computation method for these transforms. The idea of the new method is based on the double exponential transformation and the sinc approximation.
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Koichi Kondo, Shohei Sugimoto, Masashi Iwasaki
Article type: Article
2009 Volume 19 Issue 1 Pages
81-103
Published: March 25, 2009
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In this paper, we propose a new algorithm for computing SVD, with higher accuracy, of matrices with large condition number and/or multiple singular values and/or nearly multiple singular values. With the help of Newton method, we solve a nonlinear system derived from a singular vector on a plane, and an associated singular value. Choosing normal vector of the plane in orthogonal complement space of subspace spanned by obtained singular vectors, all singular-pairs are sequentially obtained by solving its nonlinear system.
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Kenichi YADANI, Kinji KIMURA, Yoshimasa NAKAMURA
Article type: Article
2009 Volume 19 Issue 1 Pages
105-120
Published: March 25, 2009
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Problem for finding the optimal PWM waveform, namely, the optimal PWM problem, is reduced to that for finding zeros of certain orthogonal polynomials. However, since the optimal PWM problem is rather ill-conditioned, one cannot solve a higher order optimal PWM problem in a double-precision floating-point number. In this note, numerical algorithms for solving optimal PWM problem on multiple-precision arithmetic are considered being based on orthogonal polynomials. Among several methods we experimented, solving a real symmetric tridiagonal matrix eigenvaule problem reduced from the optimal PWM problem is better than others with respect to speed and accuracy.
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Takahiro Onituka, Moe Thuthu, Kuniyoshi Abe, Yusuke Onoue, Seiji Fujin ...
Article type: Article
2009 Volume 19 Issue 1 Pages
121-142
Published: March 25, 2009
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A rich variety of Krylov Subspace methods are extensively used for the solution of linear systems. In particular, the investigation of the convergence of BiCG and CGS methods is a key for devising new iterative methods. In this paper, we clarify the effect of a range of initial shadow residual r^*_0 for BiCG and CGS methods. We propose using r^*_0=(A^T)^mr_0 and r^*_0=(A^T)^m×(random vector), (m=0,1,2,3). Numerical experiments show that this may enhance the convergence of BiCG and CGS methods.
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Article type: Appendix
2009 Volume 19 Issue 1 Pages
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Article type: Appendix
2009 Volume 19 Issue 1 Pages
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Article type: Appendix
2009 Volume 19 Issue 1 Pages
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Article type: Cover
2009 Volume 19 Issue 1 Pages
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Published: March 25, 2009
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Article type: Cover
2009 Volume 19 Issue 1 Pages
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Published: March 25, 2009
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