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.
@article{mc2178,
author = {Zarmehi, Fatemeh and Tavakoli, Ali},
title = {On solving operator equations by Galerkin's method with Gabor frame},
journal = {Mathematical Communications},
volume = {23},
number = {2},
year = {2018},
pages = { 227-245},
language = {eng},
url = {http://dml.mathdoc.fr/item/mc2178}
}
Zarmehi, Fatemeh; Tavakoli, Ali. On solving operator equations by Galerkin's method with Gabor frame. Mathematical Communications, Tome 23 (2018) no. 2, pp. 227-245. http://gdmltest.u-ga.fr/item/mc2178/