Frequently, one needs to evaluate expressions of the form [p(A)]  \Gamma1  q(A)b, where  A 2 R  N \ThetaN  , b 2 R  N  and p; q are polynomialswith degree q  degree p. Algorithms based on the partial fraction representation of q=p when evaluating [p(A)]  \Gamma1  q(A)b  lend themselves to parallelism but may yield poor accuracy. We discuss how to determine an incomplete partial fraction representation of q=p to achieve accuracy and examine its effects on the parallelism