Extension of the Lanczos-Phillips algorithm with Laurent biorthogonal polynomials and its application to the Thron continued fractions

Abstract

The new Lanczos-Phillips type algorithm for computing the LDU decompositions of non-Hermitian Toeplitz matrices is presented by using Laurent biorthogonal polynomials. It can be applied to computation of the Thron continued fractions which are related to two point Padé approximations. We see that the new algorithm can compute the Thron continued fractions faster and more stably than the FG algorithm does.