Abstract
Frequently, one needs to evaluate expressions of the form [ p( A)] −1 q( A) b, where A ∈ R N × N , b ∈ R N , and p and q are polynomials with degree q ⩽ degree p, and such that no zero of p is an eigenvalue of A. Algorithms based on the partial fraction representation of q p when evaluating [ p( A)] −1 q( A) b lend themselves well to implementation on a parallel computer, but might yield poor accuracy. We discuss how to determine an incomplete partial fraction representation of q p which allows parallel computation, while retaining high accuracy.
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