著者

岩田 覚

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.20, no.2, 2010-06-25

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

薩摩 順吉 時弘 哲治

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.9, no.3, pp.236-246, 1999-09-16

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Cellular automata exhibiting solitonical behavior are discussed. Then it is shown that such cellular automata are directly related to a class of nonlinear wave equations by means of the technique of "ultradiscretization". Mathematical meaning and applications to other equations of the technique are also mentioned.

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

徳永 隆治 松本 隆 徳田 功

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.7, no.4, pp.271-282, 1997-12-15

被引用文献数

1

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This paper reports a simple algorithm for reconstructing bifurcation diagrams only from time-wave forms of a parameterized family of dynamical systems, without knowing an explicit form of the dynamics and its dependence on the parameters. The algorithm consists of two steps. First, nonlinear predictors are sought using a particular class of nonlinear functions with a lot of model parameters. Second, significant parameters contributing the bifurcation are found by the principal component analysis. Using the parameterized family of nonlinear predictors, it is possible to obtain bifurcation diagram qualitatively similar to that of the original systems. The algorithm is tested against Henon equation and Rossler equation.

著者

安藤 英俊 藤木 史朗 鳥山 孝司

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.20, no.2, pp.107-116, 2010-06-25

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Many Preconditioning algorithms for Krylov subspace methods are developed and well tested on parallel computing environment like PC clusters, but performance of those methods on GPU differs from those on clusters. Although incomplete LU decomposition is the most popular preconditioner for Krylov subspace methods on CPU, its implementation on GPU was never successful because of the sequential nature of the algorithm. By using C for CUDA environment, we have efficiently implemented ILU(0) on GPU. We have also implemented and evaluated various kinds of preconditioning methods for Krylov subspace solvers on GPU, including Jacobi, Red-Black Gauss-Seidel, Line-by-Line and ILU(0). ILU(0) preconditioner turned out to be most efficient and fastest among these preconditioners when solving Poisson equation.

著者

恩田 智彦

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.5, no.1, pp.73-74, 1995-03-15

著者

深畑 幸俊

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.84-96, 2009-06-25

被引用文献数

1

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粘弾性の問題を取り扱う際に対応原理がよく用いられる.本稿では,対応原理にラプラス変換の最終値定理を併せて用いることで,粘性緩和完了後の解などが煩雑な粘弾性の計算を経ずに,弾性問題の解から直接に得られることを示す.

著者

下山 武司 伊豆 哲也 小暮 淳

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.1, pp.28-32, 2009-03-25

参考文献数

17

著者

須田 礼仁

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.21, no.2, 2011-06-24

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

岩見 真吾 佐藤 佳 小柳 義夫

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.22, no.2, pp.85-94, 2012-06-26

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Recently, in order to investigate the fundamental phenomena in immunology and virology such as maintenance of immune memory, T-cell homeostasis, the relationship between aging and immunosenescence, the regulation of the adaptive immune response during viral infection, the pathogenesis of CD4^+ depletion in HIV infection, and the underlying mechanisms of leukemia, we successfully quantied lymphocyte kinetics in humanized mice through BrdUlabeling experiment. It is worth noting that our findings are the first to assess lymphocyte dynamics utilizing this technique. At first, we will briefly give an outline of the "Quantification system of lymphocyte kinetics in humanized mice" and then we will discuss about properties of the lymphocyte kinetics and utilities of our established system.

著者

宮本 雅彦

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.17, no.1, pp.65-68, 2007-03-26

著者

杉原 厚吉

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.1, no.4, pp.280-299, 1991-12-16

被引用文献数

12

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New approaches are presented to the problem of topological inconsistency caused by geometric algorithms implemented in finite-precision arithmetic. In geometric computation numerical errors often create inconsistency in topological structures and thus cause theoretically correct algorithms to fail. To overcome this problem two approaches are considered for the case of constructing the Voronoi diagram as an example. In the first approach, higher-precision arithmetic is used to construct a closed world in which topological structures are judged always precisely, and the symbolic perturbation technique is employed to avoid complicated branches of processing for degenerate cases. In the second approach, the highest priority is placed on the maintenance of topological consistency and numerical results are used as lower-priority information; the resultant algorithm is robust in the sense that inconsistency never arises and is correct in the sense that the output converges to the true solution as the precision becomes higher.

著者

永持 仁

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.8, no.1, pp.20-29, 1998-03-16

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The connectivity augmentation problem asks to add to a given graph the smallest number of new edges so that the edge- (or vertex-) connectivity of the graph increases up to a specified value k. The problem is first studied by K. P. Eswaran and R. E. Tarjan in 1976, and both type of connectivity augmentation problems for k=2 are shown to be polynomially solvable. Afterwards, in 1987 T. Watanabe and A. Nakamura proved that the problem of making a given graph k-edge-connected by adding the smallest number of edges can be solved in O(k^2(kn+m)n^4) time for general k, where n and m are the number of vertices and edges in the input graph, respectively. Recently, a significantly faster O(nm log n+n^2 log^2 n) time algorithm for solving this problem is proposed by H. Nagamochi and T. Ibaraki by applying L. Lovasz's edge-splitting theorem. This note first reviews this alogorithm and then shows how to modify the algorithm to solve the edgeconnectivity augmentation problem for a graph with real-weighted edges.

著者

村上 征勝

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.22, no.2, pp.146-150, 2012-06-26

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

藤原 毅夫

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.1, no.2, pp.117-134, 1991-06-14

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Quasicrystals are newly discovered equiliblate systems, showing diffraction patterns of the sharp and densely distributed spots with the crystallographically disallowed symmetry. These materials open a new field of condensed matter physics. Mathematical aspects of quasicrystals are briefly reviewed, including several general methods constructing quasiperiodic systems, generalized crystallography and fractal character of electronic structures.