An improved non-linear method for the computation of a structured low rank approximation of the Sylvester resultant matrix

This paper reports on improvements to recent work on the computation of a structured low rank approximation of the Sylvester resultant matrix S(f,g)S(f,g) of two inexact polynomials f=f(y)f=f(y) and g=g(y)g=g(y). Specifically, it has been shown in previous work that these polynomials must be processed before a structured low rank approximation of S(f,g)S(f,g) is computed. The existing algorithm may still, however, yield a structured low rank approximation of S(f,g)S(f,g), but not a structured low rank approximation of S(g,f)S(g,f), which is unsatisfactory. Moreover, a structured low rank approximation of S(f,g)S(f,g) must be equal to, apart from permutations of its columns, a structured low rank approximation of S(g,f)S(g,f), but the existing algorithm does not guarantee the satisfaction of this condition. This paper addresses these issues by modifying the existing algorithm, such that these deficiencies are overcome. Examples that illustrate these improvements are shown.