An approximation formula in Hilbert space (with Z. Zhang), in Recent Advances in Computational Sciences (P. Jorgensen, X. Shen, C.-W. Shu, and N. Yan eds.), pp.218-227, World Scientific, 2008.

Abstract

Let { φk }kN be a frame for Hilbert space H. The purpose of this paper is to present an approximation formula for any f in H by a linear combination of finitely many frame elements in the frame { φk }kN and show that the obtained approximation error depends on the bounds of frame and the convergence rate of frame coefficients of f as well as the relation among the frame elements.

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