Linear algebra and its applications vol:282 issue:1-3 pages:275-295
We propose a new O(n(2)) algorithm for solving complex n x n linear systems that have Hankel structure. Via FFTs the Hankel system is transformed into a Loewner system. An inversion formula enables us to calculate the inverse of the Loewner matrix explicitely. The parameters that occur in this inversion formula are calculated by solving two rational interpolation problems on the unit circle. We present an O(n2) algorithm to solve these interpolation problems. One of the advantages of this algorithm is that it incorporates pivoting. We have implemented our Hankel solver in Fortran 90. Numerical examples are included. They show the effectiveness of our pivoting strategy. (C) 1998 Elsevier Science Inc. All rights reserved.