Recycling Krylov Subspaces for Sequences of Linear Systems

Many problems in engineering and physics require the solution of a large sequence of linear systems. We can reduce the cost of solving subsequent systems in the sequence by recycling information from previous systems. We consider two di erent approaches. For several model problems, we demonstrate that we can reduce the iteration count required to solve a linear system by a factor of two. We consider both Hermitian and non-Hermitian problems, and present numerical experiments to illustrate the e ects of subspace recycling.