共查询到20条相似文献,搜索用时 78 毫秒
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组合计数的群论与计算机方法 总被引:4,自引:0,他引:4
本文综述组合数学和图论中解决计数问题的群论与计算机方法及其最新发展。传统的计数方法得到有限的计数公式或递推公式等,然而许多复杂的问题很难得到有限的表达式,即使能得到,公式也往往非常复杂。由于计算机技术的发展不仅使复杂的计数公式有了实际意义,而且可以设计恰当的计算方法进行数值计算,使计数问题有更为广阔的发展领域。另一方面,为了计算不同构的图或组合结构,最有效的方法是群论方法,因此把群论方法与计算机方 相似文献
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Bautin焦点量公式的简单推导 总被引:2,自引:0,他引:2
本文对二次系统Bautin焦点量V3,V5,V7的表达式进行了重新推导,并且纠正了V7,表达式中的错误。由于应用了计算焦占量的一类新的递推公式,使推导过程简洁明了,避免了以往推尼它们时所表现出的复杂性。 相似文献
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1.递推公式由二项展开式得对i求和上式左边可化为(n+1)k+1-1+Sk+1,从而有(1)由(1)式得递推公式 相似文献
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某些含有根式的递推数列问题,用三角代换法使其根式脱去非常奏效,即借助于同角三角函数的平方关系式sin^2α+cos^2α=1、1+tan^2α=secα、1+cot^2α=csc^2α以及倍角公式,将已知递推数列问题转化为角成等比数列问题,进而使问题迅速获解.观察递推公式的根式结构待征,选择恰当的三角函数将通项代换是解决问题的关键. 相似文献
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F. Khanizadeh A. V. Mikhailov Jing Ping Wang 《Theoretical and Mathematical Physics》2013,177(3):1606-1654
We review two concepts directly related to the Lax representations of integrable systems: Darboux transformations and recursion operators. We present an extensive list of integrable differential-difference equations with their Hamiltonian structures, recursion operators, nontrivial generalized symmetries, and Darboux-Lax representations. The new results include multi-Hamiltonian structures and recursion operators for integrable Volterra-type equations and integrable discretizations of derivative nonlinear Schrödinger equations such as the Kaup-Newell, Chen-Lee-Liu, and Ablowitz-Ramani-Segur (Gerdjikov-Ivanov) lattices. We also compute the weakly nonlocal inverse recursion operators. 相似文献
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A note on constrained M-estimation and its recursive analog in multivariate linear regression models
RAO Calyampudi R 《中国科学A辑(英文版)》2009,52(6):1235-1250
In this paper, the constrained M-estimation of the regression coefficients and scatter parameters in a general multivariate
linear regression model is considered. Since the constrained M-estimation is not easy to compute, an up-dating recursion procedure
is proposed to simplify the computation of the estimators when a new observation is obtained. We show that, under mild conditions,
the recursion estimates are strongly consistent. In addition, the asymptotic normality of the recursive constrained M-estimators
of regression coefficients is established. A Monte Carlo simulation study of the recursion estimates is also provided. Besides,
robustness and asymptotic behavior of constrained M-estimators are briefly discussed.
The research was supported by the Natural Sciences and Engineering Research Council of Canada 相似文献
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In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values. 相似文献
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In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values. 相似文献
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Sabine Le Borne 《Numerical Linear Algebra with Applications》2023,30(5):e2497
The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block-partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well-known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods. 相似文献
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Uncertainty theory is a new branch of mathematics concerned with the analysis of subjective indeterminacy. This paper deals with the optimal control problem for a multi-stage dynamic system in an indeterminate environment. Firstly, we formulate a practical uncertain control model based on the critical value criterion and present recursion equations for this model based on Bellman’s Principle. A special linear model is shown to illustrate how the recursion equations operate to obtain the analytical solution. Furthermore, we demonstrate a hybrid intelligent algorithm to evaluate and approximate the optimal solutions of more general cases. Finally, a discrete version of the production-inventory problem is discussed and numerically analyzed to illuminate the effectiveness of the methodology. 相似文献
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In actuarial science, Panjer recursion (1981) is used in insurance to compute the loss distribution of the compound risk models. When the severity distribution is continuous with density function, numerical calculation for the compound distribution by applying Panjer recursion will involve an approximation of the integration. In order to simplify the numerical algorithms, we apply Bernstein approximation for the continuous severity distribution function and obtain approximated recursive equations, which are used for computing the approximated values of the compound distribution. The theoretical error bound for the approximation is also obtained. Numerical results show that our algorithm provides reliable results. 相似文献
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Robert Willenbring 《Discrete Applied Mathematics》2009,157(7):1607-1614
We construct a permutation representation for RNA secondary structure. We also introduce some basic combinatorial statistics for RNA secondary structure and relate them to permutation statistics when appropriate. These statistics allow us to quantify some structural phenomena in RNA secondary structure. 相似文献
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Vincent Bouchard Joel Hutchinson Prachi Loliencar Michael Meiers Matthew Rupert 《Annales Henri Poincare》2014,15(1):143-169
The Eynard–Orantin topological recursion relies on the geometry of a Riemann surface S and two meromorphic functions x and y on S. To formulate the recursion, one must assume that x has only simple ramification points. In this paper, we propose a generalized topological recursion that is valid for x with arbitrary ramification. We justify our proposal by studying degenerations of Riemann surfaces. We check in various examples that our generalized recursion is compatible with invariance of the free energies under the transformation ${(x, y) \mapsto (y, x)}$ , where either x or y (or both) have higher order ramification, and that it satisfies some of the most important properties of the original recursion. Along the way, we show that invariance under ${(x, y) \mapsto (y, x)}$ is in fact more subtle than expected; we show that there exists a number of counterexamples, already in the case of the original Eynard–Orantin recursion, that deserve further study. 相似文献