Application of the Lanczos-Phillips algorithm to continued fractions and its extension with orthogonal polynomials

Abstract

The Lanczos-Phillips algorithm is a method to compute the Cholesky decomposition of Hankel matrices. This algorithm can compute the Chebyshev continued fraction from a given set of moments faster than the qd algorithm. Moreover, a new algorithm to compute the Perron continued fraction is presented with the help of orthogonal polynomials. The Cholesky decomposition of Toeplitz matrices plays a key role.