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有理函数积分的难点在于求出有理函数分解为部分分式之和的系数.目标是通过一个可逆矩阵求出分解系数.这种方法克服了待定系数法、极限法以及奥氏(M. V. Ostrogradsik)方法等通常方法的不足,给出的分解公式简洁明了,有利于理论分析,有利于教学实践,有利于借助计算机解决实际问题. 相似文献
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Cn空间中有界域上一种积分表示 总被引:3,自引:0,他引:3
本文应用单位分解的观点及积分表示中核函数的构造理论,得到ln空间中有界域上积分表示的一种抽象的一般形式,根据这种一般形式,可以得到至今许多区域上光滑函数和全纯函数种种已有的抽象公式和具体的积分公式. 相似文献
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《数学的实践与认识》2016,(24)
使用输出DEA模型CCR、BCC、FG、ST和WY给出了整体效率的四种分解公式,并利用分解公式判别决策单元规模收益状况(包括拥挤),是对前人研究的整体效率分解公式的一种推广和应用.使用输出DEA模型CCR相对于WY的效率分解公式,可以判断决策单元是否为规模收益不变;使用BCC相对于WY的效率分解公式,可以判别是否出现拥挤.联合使用输出DEA模型FG相对于WY的效率分解公式,和ST相对于WY的效率分解公式,可以判断决策单元是否为规模收益递增、不变、递减或拥挤. 相似文献
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文中研究了对应于α-带尺度函数的小波紧框架,这个小波紧框架是由V1中的n个函数ψ1,ψ2,...,ψn构成. 首先给出了这n个函数构成小波紧框架的充分条件, 并借助尺度函数给出了构造小波紧框架的显式公式. 如果尺度函数的符号是有理函数,则可以构造出符号为有理函数的小波紧框架. 其次给出类似于正交小波的小波紧框架的分解与重构算法,并构造了小波紧框架的数值算例. 相似文献
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将求有理分式积分的传统待定常数法推广到待定函数法,给出有理分式积分中求部分分式的公式解法,此法可解决一类有理函数的积分问题. 相似文献
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二元3带小波紧框架的构造 总被引:1,自引:0,他引:1
研究二元3带小波紧框架的结构.首先给出二元3带小波紧框架的充分条件.并给出这种小波紧框架的显式公式.若给定的尺度函数的符号函数是有理函数,则可以构造出符号函数为有理函数的小波紧框架.文中给出了数值例子,还给出了二元3带小波紧框架的分解和重构算法. 相似文献
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《Journal of Computational and Applied Mathematics》1987,17(3):309-327
A discussion is given of the problem of computing including estimates of the range of a complex rational function over a circular complex interval. For this purpose, rational circular complex centered forms are defined. Explicit formulas are given for the first few forms and these formulas are used to prove that forms of higher order are an improvement over the forms of lower order. The forms are furthermore shown to be quadratically convergent.A semi-centered form is also discussed. This form is shown to be quadratically convergent depending on some conditions on the coefficients of the polynomials defining the complex rational function.Finally, a number of numerical examples are given showing the improvements obtained using the circular centered forms as compared to simple circular complex rational function estimations. 相似文献
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Dante V. Manna Luis A. Medina Victor H. Moll Armin Straub 《Numerische Mathematik》2010,115(2):289-307
A new iterative method for high-precision numerical integration of rational functions on the real line is presented. The algorithm
transforms the rational integrand into a new rational function preserving the integral on the line. The coefficients of the
new function are explicit polynomials in the original ones. These transformations depend on the degree of the input and the
desired order of the method. Both parameters are arbitrary. The formulas can be precomputed. Iteration yields an approximation
of the desired integral with mth order convergence. Examples illustrating the automatic generation of these formulas and the numerical behaviour of this
method are given. 相似文献
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《Indagationes Mathematicae》2023,34(3):622-636
A quadrature formula is a formula computing a definite integration by evaluation at finite points. The existence of certain quadrature formulas for orthogonal polynomials is related to interesting problems such as Waring’s problem in number theory and spherical designs in algebraic combinatorics. Sawa and Uchida proved the existence and the non-existence of certain rational quadrature formulas for the weight functions of certain classical orthogonal polynomials. Classical orthogonal polynomials belong to the Askey-scheme, which is a hierarchy of hypergeometric orthogonal polynomials. Thus, it is natural to extend the work of Sawa and Uchida to other polynomials in the Askey-scheme. In this article, we extend the work of Sawa and Uchida to the weight function of the Bessel polynomials. In the proofs, we use the Riesz–Shohat theorem and Newton polygons. It is also of number theoretic interest that proofs of some results are reduced to determining the sets of rational points on elliptic curves. 相似文献
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Following the basic principles stated by Painleve, we first revisit the process of selecting the admissible time-independent Hamiltonians H=(p12 + p22)/2 + V(q1,q2) whose some integer power qjnj (t) of the general solution is a singlevalued function of the complex time t. In addition to the well known rational potentials V of Henon-Heiles, this selects possible cases with a trigonometric dependence of V on qj. Then, by establishing the relevant confluences, we restrict the question of the explicit integration of the seven (three "cubic" plus four "quartic") rational Henon-Heiles cases to the quartic cases. Finally, we perform the explicit integration of the quartic cases, thus proving that the seven rational cases have a meromorphic general solution explicitly given by a genus two hyperelliptic function. 相似文献
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G. J. Groenewald M. A. Petersen Y. Zucker 《Integral Equations and Operator Theory》1997,28(4):466-491
For an arbitrary rational matrix function, not necessarily analytic at infinity, the existence of a right canonical Wiener-Hopf factorization is characterized in terms of a left canonical Wiener-Hopf factorization. Formulas for the factors in a right factorization are given in terms of the formulas for the factors in a given left factorization. All formulas are based on a special representation of a rational matrix function involving a quintet of matrices. 相似文献
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《Journal of Computational and Applied Mathematics》2001,127(1-2):67-91
Classical interpolatory or Gaussian quadrature formulas are exact on sets of polynomials. The Szegő quadrature formulas are the analogs for quadrature on the complex unit circle. Here the formulas are exact on sets of Laurent polynomials. In this paper we consider generalizations of these ideas, where the (Laurent) polynomials are replaced by rational functions that have prescribed poles. These quadrature formulas are closely related to certain multipoint rational approximants of Cauchy or Riesz–Herglotz transforms of a (positive or general complex) measure. We consider the construction and properties of these approximants and the corresponding quadrature formulas as well as the convergence and rate of convergence. 相似文献
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U. Fidalgo Prieto J. R. Illán González G. López Lagomasino 《Numerische Mathematik》2007,106(1):99-128
We discuss the convergence and numerical evaluation of simultaneous quadrature formulas which are exact for rational functions.
The problem consists in integrating a single function with respect to different measures using a common set of quadrature
nodes. Given a multi-index n, the nodes of the integration rule are the zeros of the multi-orthogonal Hermite–Padé polynomial with respect to (S, α, n), where S is a collection of measures, and α is a polynomial which modifies the measures in S. The theory is based on the connection between Gauss-type simultaneous quadrature formulas of rational type and multipoint
Hermite–Padé approximation. The numerical treatment relies on the technique of modifying the integrand by means of a change
of variable when it has real poles close to the integration interval. The output of some tests show the power of this approach
in comparison with other ones in use. 相似文献
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In this paper we give exact formulas for the potential associated to a Sturm-Liouville equation when the reflection coefficient function is rational. The solution is given in terms of a minimal realization of the reflection coefficient function.Dedicated to the memory of M.G. Kreîn 相似文献
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We present a universal formula for the dimension of the Cartan powers of the adjoint representation of a complex simple Lie algebra (i.e., a universal formula for the Hilbert functions of homogeneous complex contact manifolds), as well as several other universal formulas. These formulas generalize formulas of Vogel and Deligne and are given in terms of rational functions where both the numerator and denominator decompose into products of linear factors with integer coefficients. We discuss consequences of the formulas including a relation with Scorza varieties. 相似文献