FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1966156785> ?p ?o ?g. }

• W1966156785 endingPage "982" @default.
• W1966156785 startingPage "956" @default.
• W1966156785 abstract "The classical perturbation theory for Hermitian matrix eigenvalue and singular value problems provides bounds on the absolute differences between approximate eigenvalues (singular values) and the true eigenvalues (singular values) of a matrix. These bounds may be bad news for small eigenvalues (singular values), which thereby suffer worse relative uncertainty than large ones. However, there are situations where even small eigenvalues are determined to high relative accuracy by the data much more accurately than the classical perturbation theory would indicate. In this paper, we study how eigenvalues of a Hermitian matrix A change when it is perturbed to $wtd A=D^*AD$, where D is close to a unitary matrix, and how singular values of a (nonsquare) matrix B change when it is perturbed to $wtd B=D_1^*BD_2$, where D1 and D2 are nearly unitary. It is proved that under these kinds of perturbations small eigenvalues (singular values) suffer relative changes no worse than large eigenvalues (singular values). Many well-known perturbation theorems, including the Hoffman--Wielandt and Weyl--Lidskii theorems, are extended." @default.
• W1966156785 created "2016-06-24" @default.
• W1966156785 creator A5011252539 @default.
• W1966156785 date "1998-10-01" @default.
• W1966156785 modified "2023-09-25" @default.
• W1966156785 title "Relative Perturbation Theory: I. Eigenvalue and Singular Value Variations" @default.
• W1966156785 cites W1970377488 @default.
• W1966156785 cites W1971398013 @default.
• W1966156785 cites W1977271127 @default.
• W1966156785 cites W2003670573 @default.
• W1966156785 cites W2008942408 @default.
• W1966156785 cites W2009034807 @default.
• W1966156785 cites W2033227498 @default.
• W1966156785 cites W2035378988 @default.
• W1966156785 cites W2037561790 @default.
• W1966156785 cites W2040528593 @default.
• W1966156785 cites W2046164006 @default.
• W1966156785 cites W2046402929 @default.
• W1966156785 cites W2061116309 @default.
• W1966156785 cites W2063616005 @default.
• W1966156785 cites W2064980127 @default.
• W1966156785 cites W2065197309 @default.
• W1966156785 cites W2068844053 @default.
• W1966156785 cites W2069801226 @default.
• W1966156785 cites W2077166865 @default.
• W1966156785 cites W2081102151 @default.
• W1966156785 cites W2109624367 @default.
• W1966156785 cites W2166259197 @default.
• W1966156785 cites W4237384699 @default.
• W1966156785 doi "https://doi.org/10.1137/s089547989629849x" @default.
• W1966156785 hasPublicationYear "1998" @default.
• W1966156785 type Work @default.
• W1966156785 sameAs 1966156785 @default.
• W1966156785 citedByCount "113" @default.
• W1966156785 countsByYear W19661567852012 @default.
• W1966156785 countsByYear W19661567852013 @default.
• W1966156785 countsByYear W19661567852014 @default.
• W1966156785 countsByYear W19661567852015 @default.
• W1966156785 countsByYear W19661567852016 @default.
• W1966156785 countsByYear W19661567852017 @default.
• W1966156785 countsByYear W19661567852018 @default.
• W1966156785 countsByYear W19661567852019 @default.
• W1966156785 countsByYear W19661567852020 @default.
• W1966156785 countsByYear W19661567852021 @default.
• W1966156785 countsByYear W19661567852022 @default.
• W1966156785 countsByYear W19661567852023 @default.
• W1966156785 crossrefType "journal-article" @default.
• W1966156785 hasAuthorship W1966156785A5011252539 @default.
• W1966156785 hasBestOaLocation W19661567852 @default.
• W1966156785 hasConcept C105671362 @default.
• W1966156785 hasConcept C106487976 @default.
• W1966156785 hasConcept C109282560 @default.
• W1966156785 hasConcept C121332964 @default.
• W1966156785 hasConcept C134306372 @default.
• W1966156785 hasConcept C158693339 @default.
• W1966156785 hasConcept C159985019 @default.
• W1966156785 hasConcept C165160513 @default.
• W1966156785 hasConcept C17744445 @default.
• W1966156785 hasConcept C177918212 @default.
• W1966156785 hasConcept C192562407 @default.
• W1966156785 hasConcept C199539241 @default.
• W1966156785 hasConcept C202444582 @default.
• W1966156785 hasConcept C28940832 @default.
• W1966156785 hasConcept C33923547 @default.
• W1966156785 hasConcept C46865736 @default.
• W1966156785 hasConcept C62520636 @default.
• W1966156785 hasConcept C67820243 @default.
• W1966156785 hasConcept C78045399 @default.
• W1966156785 hasConcept C94940 @default.
• W1966156785 hasConcept C96214315 @default.
• W1966156785 hasConceptScore W1966156785C105671362 @default.
• W1966156785 hasConceptScore W1966156785C106487976 @default.
• W1966156785 hasConceptScore W1966156785C109282560 @default.
• W1966156785 hasConceptScore W1966156785C121332964 @default.
• W1966156785 hasConceptScore W1966156785C134306372 @default.
• W1966156785 hasConceptScore W1966156785C158693339 @default.
• W1966156785 hasConceptScore W1966156785C159985019 @default.
• W1966156785 hasConceptScore W1966156785C165160513 @default.
• W1966156785 hasConceptScore W1966156785C17744445 @default.
• W1966156785 hasConceptScore W1966156785C177918212 @default.
• W1966156785 hasConceptScore W1966156785C192562407 @default.
• W1966156785 hasConceptScore W1966156785C199539241 @default.
• W1966156785 hasConceptScore W1966156785C202444582 @default.
• W1966156785 hasConceptScore W1966156785C28940832 @default.
• W1966156785 hasConceptScore W1966156785C33923547 @default.
• W1966156785 hasConceptScore W1966156785C46865736 @default.
• W1966156785 hasConceptScore W1966156785C62520636 @default.
• W1966156785 hasConceptScore W1966156785C67820243 @default.
• W1966156785 hasConceptScore W1966156785C78045399 @default.
• W1966156785 hasConceptScore W1966156785C94940 @default.
• W1966156785 hasConceptScore W1966156785C96214315 @default.
• W1966156785 hasIssue "4" @default.
• W1966156785 hasLocation W19661567851 @default.
• W1966156785 hasLocation W19661567852 @default.
• W1966156785 hasOpenAccess W1966156785 @default.
• W1966156785 hasPrimaryLocation W19661567851 @default.
• W1966156785 hasRelatedWork W15049398 @default.
• W1966156785 hasRelatedWork W1995356329 @default.

• next