We give a recipe for deriving local spline approximation methods which reproduce the whole spline space. The methods are obtained by solving a series of local approximation problems. Examples of speci c quadratic and cubic approximation methods are given. x

Integral equations play an important role for their applications in practical engineering and applied science, nonlinear Urysohn integral can be when solving many problems physics, potential theory electrostatics, engineering, economics. The aim of this paper is the use spline quasi-interpolating operators space splines degree d class Cd−1 on uniform partitions a bounded interval numerical solu...

In polynomial and spline interpolation the k-th derivative of the interpolant, as a function of the mesh size h, typically converges at the rate of O(hd+1−k) as h → 0, where d is the degree of the polynomial or spline. In this paper we establish, in the important cases k = 1, 2, the same convergence rate for a recently proposed family of barycentric rational interpolants based on blending polyn...

A personal account of the author's encounters with multivariate splines during their early history. 1 Tensor product spline interpolation My first contact with multivariate splines occurred in August 1960. In my first year at the Harvard Graduate School, working as an RA for Garrett Birkhoff, I had not done too well but, nevertheless, had gotten married and so needed a better income than the RA...