Structured total least norm and approximate GCDs of inexact polynomials

Abstract: The determination of an approximate greatest common divisor (GCD) of two inexact polynomials and arises in several applications, including signal processing and control. This approximate GCD can be obtained by computing a structured low rank approximation of the Sylvester resultant matrix . In this paper, the method of structured total least norm (STLN) is used to compute a low rank approximation of , and it is shown that important issues that have a considerable effect on the approximate GCD have not been considered. For example, the established works only yield one matrix , and therefore one approximate GCD, but it is shown in this paper that a family of structured low rank approximations can be computed, each member of which yields a different approximate GCD. Examples that illustrate the importance of these and other issues are presented. [Copyright &y& Elsevier]