A Class of Local Explicit Many-Knot Spline Interpolation Schemes.

Abstract : The purpose of this paper is to present a new local explicit method for an approximation of real-valued functions defined on intervals. The operators of the form Qf = sum over (lambda sub i) (f/q sub i,k) are studied under a uniform mesh, where (q sub i,k) comes from a linear combination of B-splines. This paper contains the definition of (q sub i,k), comments on its existence, proof of reproduction of the operator Q for appropriate classes of polynomials, and a note about some applications. (Author)