Asymptotic relationships between singular values of structured matrices similarly generated by different formal expansions of a rational function

摘要

We define a class of formal expansions a Sigma(l)(infinity)=-infinity alpha(l)z(l) of a rational function with at least one non-zero pole. To distinct formal expansions Sigma(l)(infinity)=-infinity alpha(l)z(l) and Sigma(l)(infinity)=-infinity beta(l)z(l) in this class we associate structured arrays A = (alpha(ij))(i,j=1)(infinity) and B = (b(ij))(i,j=1)(infinity), defined by a(ij) = Sigma(nu=1)(k) a(nu)alpha(p nu i+qj+tau nu), and b(ij) = Sigma(nu=1)(k) a(nu)beta(pv+qj+tau v), where q (not equal 0), p(1),...p(k), and tau(1),...tau(k) are integers and a(1),...,a(k) are non-zero complex constants. We study the asymptotic relationship between the singular values of the matrices (a(ij))(1 <= i <= hn, 1 <= j <= kn) and (b(ij))(1 <= i <= hn, 1 <= j <= kn) as min(h(n), k(n)) -> infinity. Copyright (c) 2004 John Wiley W Sons, Ltd.