著者

片桐 孝洋

出版者

一般社団法人日本応用数理学会

雑誌

応用数理 (ISSN:09172270)

巻号頁・発行日

vol.19, no.2, pp.115-116, 2009-06-25

著者

相島 健助 松尾 宇泰 室田 一雄 杉原 正顕

出版者

一般社団法人日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:09172246)

巻号頁・発行日

vol.17, no.2, pp.97-131, 2007-06-25

被引用文献数

3

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Convergence theorems are established with mathematical rigour for two algorithms for the computation of singular values of bidiogonal matrices: the differential quotient difference with shift (dqds) and the modified discrete Lotka-Volterra with shift (mdLVs). Global convergence is guaranteed under a fairly general assumption on the shift, and the asymptotic rate of convergence is 1.5 for the Johnson bound shift. This result for the mdLVs algorithm is a substantial improvement of the convergence analysis by Iwasaki and Nakamura. Numerical examples support these theoretical results.

著者

平山 弘 小宮 聖司 佐藤 創太郎

出版者

一般社団法人日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:09172246)

巻号頁・発行日

vol.12, no.1, pp.1-8, 2002-03-15

被引用文献数

11

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The arithmetic operations and functions of Taylor series can be defined by C++ language. The functions which consist of arithmetic operations, pre-defined functions and conditional statements can be expanded in Taylor series. Using this, the solution of an ordinary differential equation can be expanded in Taylor series. The solution can be expanded up to arbitrary order, so the calculation formula of arbitrary order can be used instead of Runge-Kutta formula. Taylor series can be used for the evaluations of the errors and the optimal step size within given error allowance easily. In addition, we can transform Taylor series into Pade series, which give arbitrary order, high precision and A-stable formula for solving ordinary differential equation numerically.

著者

増田 直紀 巳波 弘佳 今野 紀雄

出版者

一般社団法人日本応用数理学会

雑誌

応用数理 (ISSN:09172270)

巻号頁・発行日

vol.16, no.1, pp.2-16, 2006-03-28

被引用文献数

3

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Recently, complex networks have drawn increasing interests. It is often convenient to regard this research area to be composed of studies of network structure and network functions. Studies of network structure are concerned about topological characteristics of complex networks such as the small-world and scale-free properties. Studies of network functions deal with processes and phenomena on complex networks such as virus propagation. This article is a minireview of complex networks from these dual viewpoints.

著者

片山 幹基 木村 欣司 高田 雅美 坪井 洋明 岩崎 雅史 中村 佳正

出版者

一般社団法人日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:09172246)

巻号頁・発行日

vol.18, no.3, pp.389-407, 2008-09-25

被引用文献数

1

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本論文では,上2重対角行列の高速特異値分解法1-SVDにおける左特異ベクトル計算部を改善し,直交性の優れた精度のよい左特異ベクトルを高速に求める新たな手法を定式化する.さらに,その有効性を数値実験により評価する.

著者

山本 有作

出版者

一般社団法人日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:09172246)

巻号頁・発行日

vol.16, no.4, pp.507-534, 2006-12-25

被引用文献数

1

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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.

著者

山本 有作

出版者

一般社団法人日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:09172246)

巻号頁・発行日

vol.15, no.2, pp.181-208, 2005-06-25

被引用文献数

6

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The Algorithm of Multiple Relatively Robust Representations (MR^3) is a new algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem proposed by I. Dhillon in 1997. It has attracted much attention because it can compute all the eigenvectors of an n×n matrix in only O(n^2) work and is easy to parallelize. In this article, we survey the papers related to the MR^3 algorithm and try to present a simple and easily understandable picture of the algorithm by explaining, one by one, its key ingredients such as the relatively robust representations of a symmetric tridiagonal matrix, the dqds algorithm for computing accurate eigenvalues and the twisted factorization for computing accurate eigenvectors. Limitations of the algorithm and directions for future research are also discussed.