OPTIMUM PARAMETERS FOR THE GENERALIZED ADI METHOD

In the context of the generalized ADI method, we, are concerned with t he problem of finding in the set of rational functions r with numerato r degree m and denominator degree n an element r that minimizes GRAPH ICS where E, F are disjoint real intervals. By extending a recent anal ysis by Levin and Saff, we present an explicit formula for choosing th e pair (m, n) for given m + n. Furthermore, we provide a characterizat ion of r and a Remes type algorithm for its determination. Extensive numerical computations furnish some comparison of r with asymptotical ly optimal solutions based on Fejer-Walsh and Leja-Bagby points.