The barycentric weights of rational interpolation with prescribed poles

[摘要] We introduce a method for calculating rational interpolants when some (but not necessarily all) of their poles are prescribed. The algorithm determines the weights in the barycentric representation of the rationals; it simply consists in multiplying each interpolated value by a certain number, computing the weights of a rational interpolant without poles, and finally multiplying the weights by those same numbers. The supplementary cost in comparison with interpolation without poles is about (nu + 2)N, where nu is the number of poles and N the number of interpolation points. We also give a condition under which the computed rational interpolation really shows the desired poles.

[发布日期] 1997-11-28

[关键词] interpolation;rational interpolation;barycentric representation;prescribed poles