Matches in SemOpenAlex for { <https://semopenalex.org/work/W2512538700> ?p ?o ?g. }
Showing items 1 to 88 of
88
with 100 items per page.
- W2512538700 endingPage "310" @default.
- W2512538700 startingPage "291" @default.
- W2512538700 abstract "This article deduces geometric convergence rates for approximating matrix functions via inverse-free rational Krylov methods. In applications one frequently encounters matrix functions such as the matrix exponential or matrix logarithm; often the matrix under consideration is too large to compute the matrix function directly, and Krylov subspace methods are used to determine a reduced problem. If many evaluations of a matrix function of the form f ( A ) v with a large matrix A are required, then it may be advantageous to determine a reduced problem using rational Krylov subspaces. These methods may give more accurate approximations of f ( A ) v with subspaces of smaller dimension than standard Krylov subspace methods. Unfortunately, the system solves required to construct an orthogonal basis for a rational Krylov subspace may create numerical difficulties and/or require excessive computing time. This paper investigates a novel approach to determine an orthogonal basis of an approximation of a rational Krylov subspace of (small) dimension from a standard orthogonal Krylov subspace basis of larger dimension. The approximation error will depend on properties of the matrix A and on the dimension of the original standard Krylov subspace. We show that our inverse-free method for approximating the rational Krylov subspace converges geometrically (for increasing dimension of the standard Krylov subspace) to a rational Krylov subspace. The convergence rate may be used to predict the dimension of the standard Krylov subspace necessary to obtain a certain accuracy in the approximation. Computed examples illustrate the theory developed." @default.
- W2512538700 created "2016-09-16" @default.
- W2512538700 creator A5039999347 @default.
- W2512538700 creator A5043036710 @default.
- W2512538700 creator A5072817181 @default.
- W2512538700 creator A5074334527 @default.
- W2512538700 date "2016-12-01" @default.
- W2512538700 modified "2023-09-29" @default.
- W2512538700 title "Convergence rates for inverse-free rational approximation of matrix functions" @default.
- W2512538700 cites W1589800220 @default.
- W2512538700 cites W1964310563 @default.
- W2512538700 cites W1968044527 @default.
- W2512538700 cites W1976966412 @default.
- W2512538700 cites W1978219552 @default.
- W2512538700 cites W1982786226 @default.
- W2512538700 cites W1984347942 @default.
- W2512538700 cites W1988254772 @default.
- W2512538700 cites W2016170913 @default.
- W2512538700 cites W2017710275 @default.
- W2512538700 cites W2022226008 @default.
- W2512538700 cites W2022615414 @default.
- W2512538700 cites W2044543226 @default.
- W2512538700 cites W2050996067 @default.
- W2512538700 cites W2078440628 @default.
- W2512538700 cites W2085881863 @default.
- W2512538700 cites W2105903657 @default.
- W2512538700 cites W2107091253 @default.
- W2512538700 cites W2117799929 @default.
- W2512538700 cites W2117919754 @default.
- W2512538700 cites W2130727150 @default.
- W2512538700 cites W2150150879 @default.
- W2512538700 cites W4211077197 @default.
- W2512538700 doi "https://doi.org/10.1016/j.laa.2016.08.029" @default.
- W2512538700 hasPublicationYear "2016" @default.
- W2512538700 type Work @default.
- W2512538700 sameAs 2512538700 @default.
- W2512538700 citedByCount "2" @default.
- W2512538700 countsByYear W25125387002021 @default.
- W2512538700 countsByYear W25125387002022 @default.
- W2512538700 crossrefType "journal-article" @default.
- W2512538700 hasAuthorship W2512538700A5039999347 @default.
- W2512538700 hasAuthorship W2512538700A5043036710 @default.
- W2512538700 hasAuthorship W2512538700A5072817181 @default.
- W2512538700 hasAuthorship W2512538700A5074334527 @default.
- W2512538700 hasBestOaLocation W25125387001 @default.
- W2512538700 hasConcept C106487976 @default.
- W2512538700 hasConcept C159985019 @default.
- W2512538700 hasConcept C162324750 @default.
- W2512538700 hasConcept C192562407 @default.
- W2512538700 hasConcept C207467116 @default.
- W2512538700 hasConcept C2524010 @default.
- W2512538700 hasConcept C2777303404 @default.
- W2512538700 hasConcept C28826006 @default.
- W2512538700 hasConcept C33923547 @default.
- W2512538700 hasConcept C50522688 @default.
- W2512538700 hasConceptScore W2512538700C106487976 @default.
- W2512538700 hasConceptScore W2512538700C159985019 @default.
- W2512538700 hasConceptScore W2512538700C162324750 @default.
- W2512538700 hasConceptScore W2512538700C192562407 @default.
- W2512538700 hasConceptScore W2512538700C207467116 @default.
- W2512538700 hasConceptScore W2512538700C2524010 @default.
- W2512538700 hasConceptScore W2512538700C2777303404 @default.
- W2512538700 hasConceptScore W2512538700C28826006 @default.
- W2512538700 hasConceptScore W2512538700C33923547 @default.
- W2512538700 hasConceptScore W2512538700C50522688 @default.
- W2512538700 hasFunder F4320306076 @default.
- W2512538700 hasLocation W25125387001 @default.
- W2512538700 hasLocation W25125387002 @default.
- W2512538700 hasLocation W25125387003 @default.
- W2512538700 hasOpenAccess W2512538700 @default.
- W2512538700 hasPrimaryLocation W25125387001 @default.
- W2512538700 hasRelatedWork W2067825243 @default.
- W2512538700 hasRelatedWork W2126326770 @default.
- W2512538700 hasRelatedWork W2298446516 @default.
- W2512538700 hasRelatedWork W2363617708 @default.
- W2512538700 hasRelatedWork W2369074392 @default.
- W2512538700 hasRelatedWork W2895887426 @default.
- W2512538700 hasRelatedWork W3000024058 @default.
- W2512538700 hasRelatedWork W4287904904 @default.
- W2512538700 hasRelatedWork W4383722153 @default.
- W2512538700 hasRelatedWork W955632983 @default.
- W2512538700 hasVolume "510" @default.
- W2512538700 isParatext "false" @default.
- W2512538700 isRetracted "false" @default.
- W2512538700 magId "2512538700" @default.
- W2512538700 workType "article" @default.