%0 Journal Article
	%A Jing Meng and  Peiyong Zhu and  Houbiao Li
	%D 2014
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 93, 2014
	%T Global GMRES with Deflated Restarting for Families of Shifted Linear Systems
	%U https://publications.waset.org/pdf/10000044
	%V 93
	%X Many problems in science and engineering field require
the solution of shifted linear systems with multiple right hand
sides and multiple shifts. To solve such systems efficiently, the
implicitly restarted global GMRES algorithm is extended in this
paper. However, the shift invariant property could no longer hold over
the augmented global Krylov subspace due to adding the harmonic
Ritz matrices. To remedy this situation, we enforce the collinearity
condition on the shifted system and propose shift implicitly restarted
global GMRES. The new method not only improves the convergence
but also has a potential to simultaneously compute approximate
solution for the shifted systems using only as many matrix vector
multiplications as the solution of the seed system requires. In
addition, some numerical experiments also confirm the effectiveness
of our method.

	%P 1264 - 1269