Ela a Newton Method for Canonical Wiener-hopf and Spectral Factorization of Matrix Polynomials
نویسندگان
چکیده
The paper presents a novel Newton method for constructing canonical Wiener-Hopf factorizations of complex matrix polynomials and spectral factorizations of positive definite matrix polynomials. The factorizations are the ones needed for discrete-time linear systems and hence with respect to the unit circle. The Jacobi matrix is analyzed, and the convergence of the method is proved and tested numerically. A new class of highly ill-conditioned test polynomials is introduced, and the method is shown to manifest its very good performance also in this critical setting.
منابع مشابه
A Newton method for canonical Wiener-Hopf and spectral factorization of matrix polynomials
The paper presents a novel Newton method for constructing canonical Wiener-Hopf factorizations of complex matrix polynomials and spectral factorizations of positive definite matrix polynomials. The factorizations are the ones needed for discrete-time linear systems and hence with respect to the unit circle. The Jacobi matrix is analyzed, and the convergence of the method is proved and tested nu...
متن کاملImplementing the Iakoubovski-Merino spectral factorization algorithm using state-space methods
This note explores the basic spectral factorization method of Iakoubovski and Merino [5] using state space methods. Their method is a Newton iteration method that is similar in spirit to the method of Wilson [9]. Iakoubovski and Merino prove a convergence result however, and also provide an extended algorithm that allows for factorization when the matrix to be factored has less than full rank. ...
متن کاملNonsymmetric Algebraic Riccati Equations and Wiener-Hopf Factorization for M-Matrices
We consider the nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M -matrix. Nonsymmetric algebraic Riccati equations of this type appear in applied probability and transport theory. The minimal nonnegative solution of these equations can be found by Newton’s method and basic fixed-point iterations. The study of these equations is also closely related to th...
متن کاملA spectral method based on the second kind Chebyshev polynomials for solving a class of fractional optimal control problems
In this paper, we consider the second-kind Chebyshev polynomials (SKCPs) for the numerical solution of the fractional optimal control problems (FOCPs). Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature fo...
متن کاملA spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations
In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...
متن کامل