Abstract

Abstract. We present a compensated Horner scheme, that is an accurate and fast algorithm to evaluate univariate polynomials in floating point arithmetic. The accuracy of the computed result is similar to the one given by the Horner scheme computed in twice the working precision. This compensated Horner scheme runs at least as fast as existing implementations producing the same output accuracy. We also propose to compute in pure floating point arithmetic a valid error estimate that bound the actual accuracy of the compensated evaluation. Numerical experiments involving ill-conditioned polynomials illustrate these results. All algorithms are performed at a given working precision and are portable assuming the floating point arithmetic satisfies the IEEE-754 standard.

Citations