An algorithm for two‐variable rational interpolation suitable for matrix manipulations with the evaluation–interpolation method

Abstract

An algorithm for two-variable rational interpolation is developed. The algorithm is suitable for interpolation cases where neither the number of interpolation points nor the final degrees of the rational interpolant are known a priori. Instead, a maximum degree for the interpolant's numerator and denominator is assumed. By testing the condition number of the interpolation system's matrix at each step, the necessary reductions are made in order to cope with nonnormality and unattainability occasions. The algorithm can be used for applications of the Evaluation-Interpolation technique in matrix manipulations, such as finding the inverse of a matrix with elements rational functions of two variables. Symbolic calculations are completely avoided, thus keeping the execution time very low even if the system size is large. Most importantly, the algorithm achieves accurate function recoveries for greater polynomial degrees than other bivariate rational interpolation methods.