Fast and accurate solution of Toeplitz linear least squares problems
by
Marc Van Barel
Dept. of Computer Science, K.U.Leuven, Celestijnenlaan 200A, B-3001 Heverlee, BELGIUM
Coauthors: Georg Heinig (Kuwait University), Peter Kravanja (K.U.Leuven)

Let T be a given m ×n Toeplitz matrix, i.e.,

T=[ti-j]i=0, 1, ... , m-1j=0, 1, ... , n-1

where m >= n. We assume that T has full rank. Given the Toeplitz matrix T and an m ×1 right-hand side vector b, solving the Toeplitz linear least squares problem amounts to computing the vector x such that

|| T x - b ||2

is minimal.

In this talk, we transform the original linear algebra problem into polynomial language and solve this equivalent problem by using methods for solving certain kinds of interpolation problems for vectors of polynomials.

Date received: January 31, 2000