@ARTICLE{SSX.2014,
  author = {Kirk M. Soodhalter and Daniel B. Szyld and Fei Xue},
  title = {Krylov subspace recycling for sequences of shifted linear systems},
  journal = {Applied Numerical Mathematics},
  year = {2014},
  volume = {81C},
  pages = {105--118},
  abstract = {We study the use of Krylov subspace recycling for the solution of
	a sequence of slowly-changing families of linear systems, where each
	family consists of shifted linear systems that differ in the coefficient
	matrix only by multiples of the identity. Our aim is to explore the
	simultaneous solution of each family of shifted systems within the
	framework of subspace recycling, using one augmented subspace to
	extract candidate solutions for all the shifted systems. The ideal
	method would use the same augmented subspace for all systems and
	have fixed storage requirements, independent of the number of shifted
	systems per family. We show that a method satisfying both requirements
	cannot exist in this framework.
	
	As an alternative, we introduce two schemes. One constructs a separate
	deflation space for each shifted system but solves each family of
	shifted systems simultaneously. The other builds only one recycled
	subspace and constructs approximate corrections to the solutions
	of the shifted systems at each cycle of the iterative linear solver
	while only minimizing the base system residual. At convergence of
	the base system solution, we apply the method recursively to the
	remaining unconverged systems. We present numerical examples involving
	systems arising in lattice quantum chromodynamics.},
  doi = {10.1016/j.apnum.2014.02.006},
  keywords = {paper},
  owner = {kirk},
  timestamp = {2014.03.18},
  url = {http://arxiv.org/abs/1301.2650}
}