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Communication-optimal iterative methods
2009
Journal of Physics, Conference Series
Data movement, both within the memory system of a single processor node and between multiple nodes in a system, limits the performance of many Krylov subspace methods that solve sparse linear systems and eigenvalue problems. Here, s iterations of algorithms such as CG, GMRES, Lanczos, and Arnoldi perform s sparse matrix-vector multiplications and Ω(s) vector reductions, resulting in a growth of Ω(s) in both single-node and network communication. By reorganizing the sparse matrix kernel to
doi:10.1088/1742-6596/180/1/012040
fatcat:7h56tbf3sfgfnezaisyxkmwpbe