Discrete-time symmetric polynomial equations with complex coefficients
نویسندگان
چکیده
Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results are derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorithms are implemented in the Polynomial
منابع مشابه
Stochastic averaging for SDEs with Hopf Drift and polynomial diffusion coefficients
It is known that a stochastic differential equation (SDE) induces two probabilistic objects, namely a difusion process and a stochastic flow. While the diffusion process is determined by the innitesimal mean and variance given by the coefficients of the SDE, this is not the case for the stochastic flow induced by the SDE. In order to characterize the stochastic flow uniquely the innitesimal cov...
متن کاملRecurrences and explicit formulae for the expansion and connection coefficients in series of the product of two classical discrete orthogonal polynomials
Suppose that for an arbitrary function $f(x,y)$ of two discrete variables, we have the formal expansions. [f(x,y)=sumlimits_{m,n=0}^{infty }a_{m,n},P_{m}(x)P_{n}(y),] $$ x^{m}P_{j}(x)=sumlimits_{n=0}^{2m}a_{m,,n}(j)P_{j+m-n}(x),$$ we find the coefficients $b_{i,j}^{(p,q,ell ,,r)}$ in the expansion $$ x^{ell }y^{r},nabla _{x}^{p}nabla _{y}^{q},f(x,y)=x^{ell }y^{r}f^{(p,q)}(x,y) =sumli...
متن کاملA circular stability test for general polynomials *
Abstruct: We extend a new stability test proposed recently for discrete system polynomials [l] to polynomials with complex coefficients. The method is based on a three-term recursion of a conjugate symmetric sequence of polynomials. The complex version has the same relative improved efficiency as the real version in comparison to the classical Schur-Cohn formulation for counting the number of z...
متن کاملStability Testing of 2-D Discrete Linear Systems by Telepolation of an Immittance-Type Tabular Test
A new procedure for deciding whether a bivariate (two-dimensional, 2-D) polynomial with real or complex coefficients does not vanish in the closed exterior of the unit bi-circle (is “2-D stable”) is presented. It simplifies a recent immittance-type tabular stability test for 2-D discrete-time systems that creates for a polynomial of degree ( 1 2) a sequence of 2 (or 1) centro-symmetric 2-D poly...
متن کاملDiscrete Galerkin Method for Higher Even-Order Integro-Differential Equations with Variable Coefficients
This paper presents discrete Galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. We use the generalized Jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. Numerical results are presented to demonstrate the effectiven...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Kybernetika
دوره 38 شماره
صفحات -
تاریخ انتشار 2002