Low-synch Gram–Schmidt with delayed reorthogonalization for Krylov solvers

The parallel strong-scaling of iterative methods is often determined by the number global reductions at each iteration. Low-synch Gram–Schmidt algorithms are applied here to Arnoldi algorithm reduce and therefore improve solvers for nonsymmetric matrices such as GMRES Krylov–Schur methods. In context, QR factorization “left-looking” processes one column a time. Among generating an orthogonal basis algorithm, classical with reorthogonalization (CGS2) requires three per A new variant CGS2 that only reduction iteration presented algorithm. Delayed (DCGS2) employs minimum (one) one-column at-a-time main idea behind group rearranging order operations. DCGS2 must be carefully integrated into expansion or solver. Numerical stability experiments assess robustness eigenvalue computations. Performance on ORNL Summit supercomputer then establish superiority over CGS2.