Singular value decomposition and structures total least norm for approximate greatest common divisor of unvariate polynomials

Abstract

This study presents experimental works on approximate GCD of univariate polynomials. The computation of approximate GCD is required in the case of imperfectly known or inexact data which emerges from physical measurements or previous computation error. SVD of Sylvester matrix is used to determine the degree of the approximate GCD. Then, STLN method is employed to generate an algorithm for solving the minimization problem that is to find the minimum perturbation such that the perturbed polynomials have a nonconstant GCD. The formulation of the STLN algorithm lead to the formation of LSE problem and this is solved using QR factorization. Every computation is done using MATLAB. Once the minimum perturbation is found, a MATLAB toolbox called Apalab is used to determine the coefficients of the approximate GCD. Results from experimental work performed reveal that the STLN algorithm presented is as efficient as the existing minimization algorithms.