A reorthogonalization procedure for modified Gram–Schmidt algorithm based on a rank-k update

摘要: The modified Gram–Schmidt algorithm is a well–known and widely used procedure to orthogonalize the column vectors of given matrix. When applied ill–conditioned matrices in floating point arithmetic, orthogonality among computed may be lost. In this work, we propose an posteriori reorthogonalization technique based on rank–k update vectors. level set built gets better when k increases finally reaches machine precision for large enough k. rank can tuned advance monitor quality. We illustrate efficiency approach framework Seed–GMRES solution unsymmetric linear system with multiple right–hand sides. particular, report experiments numerical simulations electromagnetic applications where rank–one sufficient recover orthogonal level.