{"paper":{"title":"Preconditioning the Restarted and Shifted Block FOM Algorithm for Matrix Exponential Computation","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Gang Wu, Hong-kui Pang, Jiang-li Sun","submitted_at":"2014-05-04T15:35:06Z","abstract_excerpt":"The approximation of $e^{tA}B$ where $A$ is a large sparse matrix and $B$ a rectangular matrix is the key ingredient in many scientific and engineering computations. A powerful tool to manage the matrix exponential function is to resort to a suitable rational approximation such as the Carath$\\acute{\\rm e}$odory-Fej$\\acute{\\rm e}$r approximation, whose core reduces to solve shifted linear systems with multiple right-hand sides. The restarted and shifted block FOM algorithm is a commonly used technique for this problem. However, determining good preconditioners for shifted systems that preserve "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0707","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}