A stabilized superfast solver for indefinite Hankel systems Original Research Article

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.