Linear algebra and its applications vol:284 issue:1-3 pages:335-355
We present a stabilized superfast solver for indefinite Hankel systems whose size is a power of 2. The Hankel system is transformed into a Loewner system, which is solved by using an inversion formula for Loewner matrices. This explicit formula for the inverse of a Loewner matrix contains certain parameters that are computed by solving two linearized rational interpolation problems on the unit circle. The heart of our Hankel solver is a superfast algorithm to solve these interpolation problems. This algorithm is stabilized via pivoting, iterative improvement, and by giving the so-called "difficult" interpolation points an adequate treatment. We have implemented our algorithm in Fortran 90. Numerical examples illustrate the effectiveness of our approach. (C) 1998 Elsevier Science Inc. All rights reserved.