Original scientific paper
On solving operator equations by Galerkin's method with Gabor frame
Fatemeh Zarmehi
; Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
Ali Tavakoli
; Department of Mathematics, University of Mazandaran, Babolsar, Iran
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
Hrčak ID:
198691
URI
Publication date:
7.11.2018.
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