On The Problem Of Best Rational Approximation With Interpolating Constraints (I)
Jia-Kai Li 1, Guo-liang Xu 11 Computing Center, Academia Sinica, China
Received 1987-11-7 Revised Online 2006-12-10
The aim of this conjoint paper is to discuss the problem of the best rational approximation with interpolating constraints. In part I, we give the necessary and sufficient conditions for the existence of the best rational approximations and establish some characterization theorem for such approximations. The problems of uniqueness, the properties for the set of best approximations, strong uniquenness and continuity of best approximation operator are considerd in Part II. The results obatined in this paper are the completion and extension of those given in .