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In this paper are given new results within the project I started some years ago, of using inverse problems methods for recovering the values at points x0 of a continuous function f with compact support E Í Rm, when N of its values are given at the nodes xi. After showing in [1] how to obtain Shepard’s formula with two different versions of the well known Backus-Gilbert process, building averaging kernels that resemble d - ”functions” centered at the nodes and consist in linear combinations of the data representers. In the present paper I am showing how to attach a spread to the Shepard formula itself, leading to a convergence theorem concerning the recovery of the considered function.
Mathematics Subject Classification (2010): 41A30.
Keywords: Backus-Gilbert theory, Shepard’s formula, deltaness, inverse problems, moving least-squares.
