Structured total least norm and approximate GCDs of inexact polynomials

✍ Scribed by Joab R. Winkler; John D. Allan

• Book ID: 104005511
• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 223 KB
• Volume: 215
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2007.03.018

✦ Synopsis

The determination of an approximate greatest common divisor (GCD) of two inexact polynomials f = f (y) and g = g(y) arises in several applications, including signal processing and control. This approximate GCD can be obtained by computing a structured low rank approximation S * (f, g) of the Sylvester resultant matrix S(f, g). In this paper, the method of structured total least norm (STLN) is used to compute a low rank approximation of S(f, g), 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 S * (f, g), 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.