Sylvester matrix rank functions on crossed products

Structured Low Rank Approximation of a Sylvester Matrix

The task of determining the approximate greatest common divisor (GCD) of univariate polynomials with inexact coefficients can be formulated as computing for a given Sylvester matrix a new Sylvester matrix of lower rank whose entries are near the corresponding entries of that input matrix. We solve the approximate GCD problem by a new method based on structured total least norm (STLN) algorithms...

A Structured Rank - Revealing Method for Sylvester Matrix 1 )

We propose a displacement structure based rank-revealing algorithm for Sylvester matrix, then apply it to compute approximate greatest common division of two univariate polynomials with floating-point coefficients. This structured rank-revealing method is based on a stabilized version of the generalized Schur algorithm [8], and is a fast rank-revealing method in the sense that, all computations...

Fast Implementation of Low Rank Approximation of a Sylvester Matrix

In [16], authors described an algorithm based on Structured Total Least Norm (STLN) for constructing a Sylvester matrix of given lower rank and obtaining the nearest perturbed polynomials with exact GCD of given degree. For their algorithm, the overall computation time depends on solving a sequence least squares (LS) problems. In this paper, a fast implementation for solving these LS problems i...

On the numerical solution of generalized Sylvester matrix equations

‎The global FOM and GMRES algorithms are among the effective‎ ‎methods to solve Sylvester matrix equations‎. ‎In this paper‎, ‎we‎ ‎study these algorithms in the case that the coefficient matrices‎ ‎are real symmetric (real symmetric positive definite) and extract‎ ‎two CG-type algorithms for solving generalized Sylvester matrix‎ ‎equations‎. ‎The proposed methods are iterative projection metho...

Finding Near Rank Deficiency in Matrix Products