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This paper focuses on Bezout equations derived from multivariate polynomial matrices in which relationships between one primary variable and other variables are described by real entire functions. We propose a method for obtaining a solution belonging to a set of multivariate rational function matrices in which all entries are real entire functions with respect to the primary variable. The proposed method is based on a new approach that overcomes the constraints and difficulties due to many variables by expanding a class of solutions to multivariate rational function matrices. 相似文献
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秩为1矩阵的性质及应用 总被引:1,自引:0,他引:1
给出了秩1矩阵的结构,讨论了这类矩阵在矩阵运算、对角化、标准型等方面的性质,推广和改进了文[1]的一些相关结果,并指出了它的若干应用,重点讨论了一类矩阵,得到了有关结论和方法. 相似文献
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M. Morh 《Mathematical and Computer Modelling》1994,19(12):85-93
The paper presents an error-free algorithm to solve a system of linear equations with polynomial coefficients. Modular arithmetic in residual polynomial class and in residual numeric class is employed. The algorithm is iterative and well suited for implementation for computers with vector operations and fast and error-free convolutors. 相似文献
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K. Maleknejad E. Hashemizadeh B. Basirat 《Communications in Nonlinear Science & Numerical Simulation》2012,17(1):52-61
In this paper, we present a method to solve nonlinear Volterra-Fredholm-Hammerstein integral equations in terms of Bernstein polynomials. Properties of these polynomials and operational matrix of integration together with the product operational matrix are first presented. These properties are then utilized to transform the integral equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Bernstein coefficients. The method is computationally very simple and attractive and numerical examples illustrate the efficiency and accuracy of the method. 相似文献
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S. Yu. Slavyanov 《Theoretical and Mathematical Physics》2003,136(3):1251-1257
Under the assumption that potentials in two Schrödinger equations differ by a polynomial of degree k, we derive a (k+4)th-order equation for a function that is a product of solutions of these equations. Several examples of applications in physics are considered. 相似文献
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This study addresses Bezout equations over bivariate polynomial matrices, where the relationship between two variables is described by a real entire function. This paper proposes a solution method that makes optimal use of minor primeness to reduce such Bezout equations to simple equations over univariate scalar polynomials. The proposed solution method requires only matrix calculations, thus making it very useful, especially in the absence of modern computer algebra systems. 相似文献
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Wen-Xiu MA 《Frontiers of Mathematics in China》2013,8(5):1139-1156
A class of trilinear differential operators is introduced through a technique of assigning signs to derivatives and used to create trilinear differential equations. The resulting trilinear differential operators and equations are characterized by the Bell polynomials, and the superposition principle is applied to the construction of resonant solutions of exponential waves. Two illustrative examples are made by an algorithm using weights of dependent variables. 相似文献
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Complex valued systems of equations with a matrix R + 1S where R and S are real valued arise in many applications. A preconditioned iterative solution method is presented when R and S are symmetric positive semi‐definite and at least one of R, S is positive definite. The condition number of the preconditioned matrix is bounded above by 2, so only very few iterations are required. Applications when solving matrix polynomial equation systems, linear systems of ordinary differential equations, and using time‐stepping integration schemes based on Padé approximation for parabolic and hyperbolic problems are also discussed. Numerical comparisons show that the proposed real valued method is much faster than the iterative complex symmetric QMR method. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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两类循环分块矩阵及其有关算法 总被引:4,自引:0,他引:4
本文利用多项式矩阵最大右公因式,给出R-循环分块矩阵的和对称R-循环分块矩阵非奇异以及线性方程组反问题有唯一解的充要条件,进而得到它们求逆、线性方程组唯一解、线性方程组在循环分块矩阵中的反总问题求唯一解的算法。 相似文献
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An iterative algorithm for solving a class of generalized coupled Sylvester-transpose matrix equations over bisymmetric or skew-anti-symmetric matrices
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This paper presents an iterative algorithm to solve a class of generalized coupled Sylvester-transpose matrix equations over bisymmetric or skew-anti-symmetric matrices. When the matrix equations are consistent, the bisymmetric or skew-anti-symmetric solutions can be obtained within finite iteration steps in the absence of round-off errors for any initial bisymmetric or skew-anti-symmetric matrices by the proposed iterative algorithm. In addition, we can obtain the least norm solution by choosing the special initial matrices. Finally, numerical examples are given to demonstrate the iterative algorithm is quite efficient. The merit of our method is that it is easy to implement. 相似文献
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Bibhas Adhikari 《Linear and Multilinear Algebra》2013,61(5):603-616
Given a quadratic two-parameter matrix polynomial Q(λ,?μ), we develop a systematic approach to generating a vector space of linear two-parameter matrix polynomials. The purpose for constructing this vector space is that potential linearizations of Q(λ,?μ) lie in it. Then, we identify a set of linearizations and describe their constructions. Finally, we determine a class of linearizations for a quadratic two-parameter eigenvalue problem. 相似文献
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Nicole Brillouët-Belluot 《Journal of Difference Equations and Applications》2013,19(11):1237-1255
Solving the class of second order iterative-difference equations is a difficult problem, proposed as an open problem in Brillouët-Belluot [Aequationes Math. 61 (3) (2001), p. 304]. In this paper, we use three methods to approach such a class of equations, finding their affine solutions, proving the existence of their bounded continuous solutions and constructing their continuous and piecewise continuous solutions. 相似文献
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Burgers方程是一类应用广泛的非线性偏微分方程,方程中的非线性项难以处理。该文提出一种新的时空多项式配点法——多项式特解法求解三维Burgers方程。求解过程分为两步:第一步,对三维Burgers方程中的线性导数项(包括时间导数项),求出相应的多项式特解。第二步,将求出的多项式特解作为基函数,对三维Burgers方程中剩余的非线性项进行迭代求解。与时空多项式函数作为基函数对三维Burgers方程进行直接求解相比,该算法简单易行,得到的近似解精度非常高,算法极其稳定,对于教学过程中提高学生的编程能力,加深对高维Burgers方程的理解能力以及Burgers方程的实际应用具有重要意义。 相似文献