A TSQR Based Krylov Basis Computation Method on Hybrid GPU Cluster

Krylov Subspace Methods are commonly used for solving large sparse linear problems. The computation of an orthonormal subspace basis usually consumes most of the execution time in methods like Arnoldi iteration, which suffers from substantial communication overhead due to matrix-vector multiplications and vector inner products in parallel implementations. In this paper, we propose a method that combines a hypergraph based power iteration and a Tall Skinny QR factorization to form a Krylov subspace basis. Experimentation shows that our method has a lower communication cost and better numerical stability than Arnoldi iteration on CPU-GPU clusters, and an auto-tuning scheme shall be incorporated to address problems with different conditions.