نتایج جستجو برای: generalized sylvester matrix equations
تعداد نتایج: 729242 فیلتر نتایج به سال:
We revisit the two standard dense methods for matrix Sylvester and Lyapunov equations: the Bartels-Stewart method for A1X +XA2 +D = 0 and Hammarling’s method for AX + XA + BB = 0 with A stable. We construct three schemes for solving the unitarily reduced quasitriangular systems. We also construct a new rank-1 updating scheme in Hammarling’s method. This new scheme is able to accommodate a B wit...
We present an algorithm for solving polynomial equations, which uses generalized eigenvalues and eigenvectors of resultant matrices. We give special attention to the case of two bivariate polynomials and the Sylvester or Bezout resultant constructions. We propose a new method to treat multiple roots, detail its numerical aspects and describe experiments on tangential problems, which show the ef...
We propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F (s): The proposed method exploits the structure of the left null space of generalized Wolovich or Sylvester resultants to compute row polynomial vectors that form a minimal polynomial basis of left kernel of the given polynomial matrix. The entire procedure can be imple...
We propose a fast algorithm for computing approximate GCD of univariate polynomials with coefficients that are given only to a finite accuracy. The algorithm is based on a stabilized version of the generalized Schur algorithm for Sylvester matrix and its embedding. All computations can be done in O(n2) operations, where n is the sum of the degrees of polynomials. The stability of the algorithm ...
In this paper, we develop a fast structured total least squares (STLS) algorithm for computing an approximate greatest common divisor (GCD) of two univariate polynomials. By exploiting the displacement structure of the Sylvester matrix and applying the generalized Schur algorithm, each single iteration of the proposed algorithm has quadratic computational complexity in the degrees of the given ...
In this paper we obtain several results on the rank properties of Hadamard matrices (including Sylvester Hadamard matrices) as well as (generalized) Hadamard matrices. These results are used to show that the classes of (generalized) Sylvester Hadamard matrices and of generalized pseudo-noise matrices are equivalent, i.e., they can be obtained from each other by means of row/column permutations....
We propose an elegant and conceptually simple method for computing the periodic solution of three classes of periodic matrix equations | Ric-cati, Lyapunov and Sylvester. Such equations arise naturally in several problems of linear system theory. Our approach is very attractive from a numerical point of view, since it is based on the periodic Schur form of techniques involving unitary (orthogon...
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