A fast Hankel solver based on an inversion formula for Loewner matrices

AbstractWe propose a new O(n2) algorithm for solving complex n × 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