On solving operator equations by Galerkin's method with Gabor frame

Fatemeh Zarmehi; Ali Tavakoli

Vol. 23 No. 2 (2018)

Regular Articles

On solving operator equations by Galerkin's method with Gabor frame

Published 2018-01-18

Fatemeh Zarmehi
Ali Tavakoli

Fatemeh Zarmehi
Vali-e-Asr University of Rafsanjan

Ali Tavakoli
Vali-e-Asr University of Rafsanjan

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Abstract

‎This paper deals with solving boundary value problems by Galerkin's method in which we use Gabor frames as trial and test functions‎. ‎We show that‎, ‎the preconditioned stiffness matrix resulted by discretization is compressible and its sparsity‎ ‎pattern involves a bounded polyhedron structure‎. ‎Moreover‎, ‎we introduce an adaptive Richardson iterative method to‎ ‎solve the resulting system and we also show that by choosing a suitable smoothing parameter‎, ‎the method would be convergent‎.

Keywords

Gabor frame, Operator equation, Compressed matrix

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