Interpolation by Cauchy-Vandermonde systems and applications

[摘要] Cauchy-Vandermonde systems consist of rational functions with prescribed poles. They are complex ECT-systems allowing Hermite interpolation for any dimension of the basic spate. A survey of interpolation procedures using CV-systems is given, some equipped with short new proofs, which generalize the well-known formulas of Lagrange, Neville-Aitken and Newton for interpolation by algebraic polynomials. The arithmetical complexitiy is O(N-2) for N Hermits data. Also, inversion formulas for the Cauchy-Vandermonde matrix are surveyed. Moreover, a new algorithm solving the system of N linear Cauchy-Vandermonde equations for multiple nodes and multiple poles recursively is given which does not require additional partial fraction decompositions. As an application construction of rational B-splines with prescribed poles is discussed. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 41A05; 65D05.

[发布日期] 2000-10-01

[关键词] prescribed poles;Cauchy-Vandermonde systems;interpolation algorithms