%0 Journal Article
	%A Qiang Niu and  Linzhang Lu
	%D 2012
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 68, 2012
	%T Restarted GMRES Method Augmented with the Combination of Harmonic Ritz Vectors and Error Approximations
	%U https://publications.waset.org/pdf/5472
	%V 68
	%X Restarted GMRES methods augmented with approximate eigenvectors are widely used for solving large sparse linear systems. Recently a new scheme of augmenting with error approximations is proposed. The main aim of this paper is to develop a restarted GMRES method augmented with the combination of harmonic Ritz vectors and error approximations. We demonstrate that the resulted combination method can gain the advantages of two approaches: (i) effectively deflate the small eigenvalues in magnitude that may hamper the convergence of the method and (ii) partially recover the global optimality lost due to restarting. The effectiveness and efficiency of the new method are demonstrated through various numerical examples.

	%P 857 - 864