著者

緒方 秀教 杉原 正顯

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.8, no.2, pp.223-256, 1998

参考文献数

7

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Quadrature formulae for oscillatory infinite integrals involving the Bessel functions are proposed. Those formulae are obtained by the so-called double exponential type of variable transformations followed by an application of quadrature formulae whose abscissae are the zeros of the Bessel functions, which are developed in [3]. Numerical examples are included.

著者

佐藤 哲

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.421-433, 2006-12-25

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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.

著者

竹内 敏己 藤野 清次

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.5, no.1, pp.9-26, 1995

参考文献数

14

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In this paper we study theoretically on some mathematical properties of the matrix of the linear system of equations which stems from discretization of n-dimensional Laplace equation by finite difference approximations. The mathematical properties, i.e., the maximum and minimum absolute eigenvalues, the eigenvectors and the condition numbers of the coefficient matrix A and the Jacobi matrix B of the iterative method are estimated. The discretization by the finite differences in n-dimensions is made using the nearest and skewed neighboring grid points. The effectiveness of the variants of the finite differences is shown throughout this study.

著者

福田 亜希子 岩崎 雅史 山本 有作 石渡 恵美子 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.23, no.1, pp.109-181, 2013-03-25

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近年,ハングリー型の離散可積分系である離散ハングリー戸田方程式と離散ハングリーロトカ・ボルテラ系から,非対称行列の固有値が高精度に求まるアルゴリズムが定式化されている.本論文では,アルゴリズムの導出過程に加え,中心多様体理論を利用した漸近解析,浮動小数点数演算における混合誤差解析,高速化のための原点シフトに関する結果について概説する.ハングリー型の離散可積分系を結ぶベックルント変換についても示す.

著者

野津 裕史 田端 正久

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.427-445, 2008

参考文献数

29

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Navier-Stokes方程式のための,圧力安定化有限要素法と時間刻み1次精度特性曲線法を組み合わせたスキームを提案する.P1/P1要素を用いており,現れる行列は対称である.2次元および3次元問題の数値計算結果を与える.

著者

東田 憲太郎 加古 孝

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.3, pp.237-253, 2006-09-25

被引用文献数

1

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In this paper, we propose a numerical method for the voice generation process based on some mathematical model. As the model, we use Webster's horn equation for the 1D case. We then discretize this equation by FEM and calculate the frequency response function. We consider the complex eigenvalue problem corresponding to Webster's horn equation and give a variational formula for the complex eigenvalue with respect to the variation of vocal tract shape. We numerically confirm that the complex eigenvalue is closely related to the frequency response function, and propose a vocal tract shape design algorithm using variational formula and confirm its efficiency numerically.

著者

松尾 宇泰 宮武 勇登

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.22, no.3, pp.213-251, 2012-09-25

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微分方程式の数値解法のうち,微分方程式が持つ何らかの構造を離散系でも再現する特殊な数値解法のことを「構造保存数値解法」と呼ぶ.構造保存数値解法は,1980年代に常微分方程式系に対し提唱されてから長足の進歩を遂げ,最近では偏微分方程式系に対しても研究が進んでいる.本サーベイでは,これらの基礎と最近の進展について概説する.

著者

森継 修一

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.1, pp.79-92, 2006

参考文献数

16

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We show an algebraic proof of the method for solving cubic equations by ORIGAMI (paper folding). Using ORIGAMI, we can solve the construction problems that are unsolvable in Euclidean geometry, such as angle trisection and doubling cubes. In our formulation, we solve the radical membership problem in polynomial ideals computing a Grobner basis together with constraints of parameters, which correspond to geometrically degenerate cases. Consequently, cubic equations are clearly solved as construction problems. We also show the construction of another solution by trigonometric functions, that is an application of angle trisection by ORIGAMI.

著者

一森 哲男

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 = Transactions of the Japan Society for Industrial and Applied Mathematics (ISSN:09172246)

巻号頁・発行日

vol.16, no.3, pp.265-276, 2006-09-25

被引用文献数

2

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This paper discusses two apportionment methods taking account of dispersion. The first one minimizes the variance of per capita shares of a representative of 47 prefectures. And the second one minimizes the coeffcient of variation of those shares of a representative of 47 prefectures. We observe that these methods give reasonable allocations of 300 seats to 47 prefectures and also reasonable allocations of 180 to 11 blocks in Japan.

著者

武田 利浩 田中 昭吉 丹野 州宣

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.5, no.4, pp.399-409, 1995-12-15

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Various types of neural networks have been proposed, and many applications of the technology have also been vigorously promoted in the wide range of the fields. However, simulations of large scale neural networks require quite high speed computation ability because of an enormous of time in learning. Then, many studies have been reported on efficient parallel simulation of neural networks. This paper proposes parallel computing algorithm allowing the back-propagation model to be simulated upon an 8-neighbor processor array. Taking account of the parallelism intrinsically imbedded in the neural networks, the algorithm realizes high speed neural network computation. The time complexities of the algorithm are only O(NLp/P)for communications and O(N^2L/P)for computation in one step learning processing, where N is the number of the neurons in a layer, P(pxp)is the number of processors, and L is the number of the layers.

著者

塩出 亮 阿部 邦美 藤野 清次

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.1, pp.27-42, 2007-03-25

被引用文献数

2

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The MRTR method has been recognized as an effective iterative method for singular systems of linear equations. The MRTR method is based on the three-term recurrence formula of the CG method and the algorithm is proven to be mathematically equivalent to the CR method. In this paper, we extend the MRTR method to solve complex symmetric linear systems. We describe this extended cs_MRTR method and prove that this method is mathematically equivalent to the COCR method. Numerical examples show that the cs_MRTR method shows a more stable convergence behavior than the COCR method.(Theory)

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

神山 雅子

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, 2005

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.