Flexible GMRES with Analog Accelerators

The iterative solution of linear algebraic equations of the form Ax = b, A ∈ R n×n , b ∈ R n, is among the most important computational kernels in optimization, science, and engineering. In this work, we focus on solving general sparse linear systems by preconditioned Krylov subspace methods, which consider approximate solutions xm from the subspace Kj (A, b) = {r0 , AM−1 r0 ,(AM−1 ) 2 r0 , . . . ,(AM−1 ) m−1 r0}, where M ∈ R n×n approximates A−1 and r0 = b − Ax0. While research on sparse iterative solver libraries for exascale computing is active, alternatives that increase concurrency of compute nodes are highly desirable.