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

We define a class of formal expansions ∑∞ `=−∞ α`z ` of a rational function with at least one nonzero pole. To distinct formal expansions ∑∞ `=−∞ α`z ` and ∑∞ `=−∞ β`z ` in this class we associate structured arrays A = (aij) ∞ i,j=1 and B = (bij) ∞ i,j=1, defined by aij = ∑k ν=1 aναpνi+qj+τν and bij = ∑k ν=1 aνβpνi+qj+τν , where q ( 6= 0), p1, . . . , pk , and τ1, . . . , τk are integers and a1, . . . , ak are nonzero complex constants. We study the asymptotic relationship between the singular values of the matrices (aij)1≤i≤hn,1≤j≤kn and (bij)1≤i≤hn,1≤j≤kn as min(hn, kn) → ∞. Copyright c © 2000 John Wiley & Sons, Ltd. key words: Singular value; rational function; structured matrix