Accurate Evaluation of Bivariate Polynomials

Polynomials are widely used in scientific computing and engineering. In this paper, we present an accurate and fast compensated algorithm to evaluate bivariate polynomials with floating-point coefficients. This algorithm is applying error free transformations to the bivariate Horner scheme and sum the final decomposition accurately. We also prove the proposed algorithm's accuracy with forward error analysis that the accuracy of the computed result is similar to the result computed by the bivariate Horner scheme in twice the working precision. Numerical experiments illustrate the behavior and it has higher efficiency than the bivariate Horner scheme implemented in double-double library.