著者

Satoko Kikkawa Tsubasa Saito Emiko Ishiwata Hidehiko Hasegawa

出版者

一般社団法人 日本応用数理学会

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.5, pp.9-12, 2013 (Released:2013-02-24)

参考文献数

6

被引用文献数

2

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MuPAT enables the users to easily treat quadruple and octuple precision arithmetics as well as double precision arithmetic on Scilab. Using external C routines, we have also developed a high speed implementation MuPAT_c for Windows, Mac OS, and Linux. MuPAT_c reduced the computation time especially for all octuple precision arithmetic and inner product of quadruple precision arithmetic. MuPAT_c can run 90-1200 times faster than MuPAT. We applied three different precisions to tridiagonalization by the Lanczos method and confirmed that a high precision arithmetic was essential for the Lanczos method to get accurate eigenvalues of real symmetric matrices.

著者

Takahito Kashiwabara Issei Oikawa

出版者

一般社団法人 日本応用数理学会

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.5, pp.5-8, 2013 (Released:2013-02-24)

参考文献数

5

被引用文献数

1

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Non-differentiability of the absolute value function at the origin can affect the accuracy of numerical computations for the $L^1$ norm. We present an example in which the accuracy does deteriorate, and we provide a convergence order for such situations. We propose a simple algorithm to improve the convergence order, confirming its effectiveness as in the example described above. Mesh-dependent integrands and applications to finite element method are also considered.

著者

Tomoaki Okayama

出版者

一般社団法人 日本応用数理学会

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.5, pp.1-4, 2013 (Released:2013-02-07)

参考文献数

6

被引用文献数

2

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The original form of the Sinc approximation is efficient for functions whose boundary values are zero, but not for other functions. The typical way to treat general boundary values is to introduce auxiliary basis functions, and in fact such an approach has been taken commonly in the literature. However, the approximation formula in each research is not exactly the same, and still other formulas can be derived as variants of existing formulas. The purpose of this paper is to sum up those existing formulas and new ones, and to give explicit proofs of those convergence theorems.

著者

Kensuke Ishitani

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.4, pp.13-16, 2012 (Released:2012-04-16)

参考文献数

6

被引用文献数

5 5 2

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This paper presents a new methodology to compute VaR in the portfolio credit loss model. The Wavelet Approximation can be useful to compute non-smooth distributions, often arising in small or concentrated portfolios. We contribute to this technique by extending the Wavelet Approximation for Vasicek one-factor model to multi-factor model. Key features of our new algorithm are: (i) a finite series expansion of the wavelet scaling coefficients, (ii) Wynn's epsilon-algorithm to accelerate convergence of those series, and (iii) an efficient spline interpolation to calculate the Laplace transforms. We illustrate the effectiveness of our algorithm through numerical examples.

著者

Suguru Yamanaka Masaaki Sugihara Hidetoshi Nakagawa

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.3, pp.93-96, 2011 (Released:2011-12-24)

参考文献数

6

被引用文献数

2 2

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We present an intensity based credit rating migration model and execute empirical analyses on forecasting the number of downgrades in some credit portfolios. The framework of the model is based on so-called top-down approach. We firstly model economy-wide rating migration intensity with a self-exciting stochastic process. Next, we characterize the downgrade intensity for the underlying sub-portfolio with some thinning model specified by the distribution of credit ratings in the sub-portfolio. The results of empirical analyses indicate that the model is to some extent consistent with downgrade data of Japanese firms in a sample period.

著者

Akihiro Yamaguchi Takaaki Seo Keisuke Yoshikawa

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.2, pp.123-126, 2010 (Released:2010-12-10)

参考文献数

6

被引用文献数

5 10

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In this paper, the pass rate of the NIST SP800-22 statistical test suite for the ideally true random sequences is analyzed by the simulation of statistical tests, and derived by the theoretical analysis under the assumption that there are no correlation among tests. As examples of chaos based system, Vector Stream Cipher (VSC128S) and the encryption system using Arnold's cat map are tested. The test results are compared with the theoretical one for the true random sequences and validity of presented analysis is discussed.

著者

Ryo Takahashi Etsushi Nameda Ken Umeno

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.2, pp.9-12, 2010 (Released:2010-03-09)

参考文献数

9

被引用文献数

2 1

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Inner angle of triangle made of consecutive three points on unit circle is investigated. We use two methods to plot points. One is plotting random numbers whose distribution is uniform. Another is plotting consecutive numbers obtained by a map which generates complex chaotic sequences with constant power. We focus on an inner angle at the middle point in consecutive three points. An angle for chaotic sequence is found to be different from one for uniform random sequence.