Convergence Estimates For A Class Of Interpolation Approximation

The interpolation approximation is important, because the computation of inner product is avoided. This thesis studies convergence properties for a class of interpolation approximation. It consists of two parts: one is for one dimension and the other is for two dimensional case. Firstly, we prove a relation between moment condition and accuracy; Secondly, a uniform estimate for interpolation approximation is obtained; Finally, some examples are provided.The paper is organized as follows: In Chapter 1, some necessary notations, definitions, the background and the main results are given; The second chapter is devoted to studying relative results for one dimensional interpolation approximation; In the last part, the conclusions of Chapter 2 are extended to two dimensional case.