Avoiding Communication in Two-Sided Krylov Subspace Methods

Preconditioning  Krylov Subspace Methods are commonly used for solving linear system  Standard implementations are communication-bound due to required SpMV and orthogonalization in every iteration  Solution: rearrange algorithms to perform s iterations at a time without communicating (s-step methods)  SpMV in each iteration is replaced with a call to the Matrix Powers Kernel, which performs s SpMVs while reading the matrix only once  Used to generate s basis vectors for the Krylov Subspace Research supported by Microsoft (Award #024263) and Intel (Award #024894) funding and by matching funding by U.C. Discovery (Award #DIG07-10227). Additional support comes from Par Lab affiliates National Instruments, NEC, Nokia, NVIDIA, Samsung, and Sun Microsystems.