{"paper":{"title":"Bounds on changes in Ritz values for a perturbed invariant subspace of a Hermitian matrix","license":"","headline":"","cross_cats":["cs.NA","math.SP"],"primary_cat":"math.NA","authors_text":"A. V. Knyazev, C. C. Paige, I. Panayotov, M. E. Argentati","submitted_at":"2006-10-16T20:10:57Z","abstract_excerpt":"The Rayleigh-Ritz method is widely used for eigenvalue approximation. Given a matrix $X$ with columns that form an orthonormal basis for a subspace $\\X$, and a Hermitian matrix $A$, the eigenvalues of $X^HAX$ are called Ritz values of $A$ with respect to $\\X$. If the subspace $\\X$ is $A$-invariant then the Ritz values are some of the eigenvalues of $A$. If the $A$-invariant subspace $\\X$ is perturbed to give rise to another subspace $\\Y$, then the vector of absolute values of changes in Ritz values of $A$ represents the absolute eigenvalue approximation error using $\\Y$. We bound the error in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610498","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0610498/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}