Optimal Number of Required Points for Evaluation - Interpolation Technique in Complex Basis

Abstract

According to polynomial evaluation-interpolation technique, first of all, the set of required points, in which interpolation will be executed, must be defined in evaluation part. Taking into account that working in complex domain provides as with the advantage of conjugate properties, the number of evaluations at these points could be reduced. This paper presents the appropriate form of required points, aiming to an optimal reduction of their amount. The appropriate form of points for two variable polynomials depends on the degree of each variable. As a repercussion the number of evaluations could be reduced even up to the half.