From: "Neil Judell" Newsgroups: sci.math.num-analysis Subject: Re: Determinant of Toeplitz matrix Date: Sat, 20 Dec 1997 22:13:55 -0500 [This was a multi-part message in MIME format; streamlined -- djr] Uh, I guess I'm not clear on EXACTLY what you're asking. But, with respect to determinants of Toeplitz matrices, the following two things MIGHT help you in what you're looking for: 1) The determinant of a Toeplitz matrix is equal to the product of (1-|k-sub-i|^2), where k-sub-i is the i'th reflection coefficient of the Levinson recursion. 2) limit k->infinity |R_subk|^(1/k) is equal to exp((1/4*pi) loop integral z^-1 ln(|H(z)|^2) dz), where H(z) is the generating polynomial for the row of R. An excellent reference book for all kinds of lovely properties of Toeplitz Matrices is an old book "Toeplitz Matrices and their Applications" by Grenander and Szego. I'm not sure, but it may be out of print now. Does this help any? --neil serena ng wrote in message <349C3316.D780D8DA@bc.edu>... Hi I need to evaluate the determinant of a k-th order Toeplitz matrix to that of one of order k+1. This amounts to considering A1 x1^k +A2 x2^k + .... _____________ A1 x1^(k+1) + A2 x2 ^(k+1) + ..... I know as k goes to infinity this limit is 1. But does someone know what this limit is as a function of k? Thanks in advance.