Optimum parameters for the generalized ADI method

Abstract

In the context of the generalized ADI method, we are concerned with the problem of finding in the set of rational functions r with numerator degree m and denominator degree n an element r * that minimizeswhere E, F are disjoint real intervals. By extending a recent analysis by Levin and Saff, we present an explicit formula for choosing the pair (m, n) for given m + n. Furthermore, we provide a characterization of r * and a Remes type algorithm for its determination. Extensive numerical computations furnish some comparison of r * with asymptotically optimal solutions based on Fejér-Walsh and Leja-Bagby points.