FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2083095625> ?p ?o ?g. }

• W2083095625 endingPage "72" @default.
• W2083095625 startingPage "44" @default.
• W2083095625 abstract "We present some superfast ($O((m+n)log^{2}(m+n))$ complexity) and stable structured direct solvers for $mtimes n$ Toeplitz least squares problems. Based on the displacement equation, a Toeplitz matrix $T$ is first transformed into a Cauchy-like matrix $mathcal{C}$, which can be shown to have small off-diagonal numerical ranks when the diagonal blocks are rectangular. We generalize standard hierarchically semiseparable (HSS) matrix representations to rectangular ones, and construct a rectangular HSS approximation to $mathcal{C}$ in nearly linear complexity with randomized sampling and fast multiplications of $mathcal{C}$ with vectors. A new URV HSS factorization and a URV HSS solution are designed for the least squares solution. We also present two structured normal equation methods. Systematic error and stability analysis for our HSS methods is given, which is also useful for studying other HSS and rank structured methods. We derive the growth factors and the backward error bounds in the HSS factorizations, and show that the stability results are generally much better than those in dense LU factorizations with partial pivoting. Such analysis has not been done before for HSS matrices. The solvers are tested on various classical Toeplitz examples ranging from well-conditioned to highly ill-conditioned ones. Comparisons with some recent fast and superfast solvers are given. Our new methods are generally much faster, and give better (or at least comparable) accuracies, especially for ill-conditioned problems." @default.
• W2083095625 created "2016-06-24" @default.
• W2083095625 creator A5022664058 @default.
• W2083095625 creator A5047496441 @default.
• W2083095625 creator A5056635728 @default.
• W2083095625 creator A5061087485 @default.
• W2083095625 date "2014-01-01" @default.
• W2083095625 modified "2023-10-06" @default.
• W2083095625 title "Superfast and Stable Structured Solvers for Toeplitz Least Squares via Randomized Sampling" @default.
• W2083095625 cites W1628239836 @default.
• W2083095625 cites W1965867049 @default.
• W2083095625 cites W1968691112 @default.
• W2083095625 cites W1973786815 @default.
• W2083095625 cites W1973915465 @default.
• W2083095625 cites W1983103429 @default.
• W2083095625 cites W1984265227 @default.
• W2083095625 cites W1997066455 @default.
• W2083095625 cites W2002651179 @default.
• W2083095625 cites W2010961009 @default.
• W2083095625 cites W2012841869 @default.
• W2083095625 cites W2025986317 @default.
• W2083095625 cites W2033093196 @default.
• W2083095625 cites W2036564429 @default.
• W2083095625 cites W2037598393 @default.
• W2083095625 cites W2060492405 @default.
• W2083095625 cites W2065405327 @default.
• W2083095625 cites W2083903752 @default.
• W2083095625 cites W2089958289 @default.
• W2083095625 cites W2105591391 @default.
• W2083095625 cites W2114583457 @default.
• W2083095625 cites W2117756735 @default.
• W2083095625 cites W2119233169 @default.
• W2083095625 cites W2154025750 @default.
• W2083095625 cites W2158958710 @default.
• W2083095625 cites W2169370352 @default.
• W2083095625 cites W4243081751 @default.
• W2083095625 doi "https://doi.org/10.1137/120895755" @default.
• W2083095625 hasPublicationYear "2014" @default.
• W2083095625 type Work @default.
• W2083095625 sameAs 2083095625 @default.
• W2083095625 citedByCount "69" @default.
• W2083095625 countsByYear W20830956252013 @default.
• W2083095625 countsByYear W20830956252014 @default.
• W2083095625 countsByYear W20830956252015 @default.
• W2083095625 countsByYear W20830956252016 @default.
• W2083095625 countsByYear W20830956252017 @default.
• W2083095625 countsByYear W20830956252018 @default.
• W2083095625 countsByYear W20830956252019 @default.
• W2083095625 countsByYear W20830956252020 @default.
• W2083095625 countsByYear W20830956252021 @default.
• W2083095625 countsByYear W20830956252022 @default.
• W2083095625 countsByYear W20830956252023 @default.
• W2083095625 crossrefType "journal-article" @default.
• W2083095625 hasAuthorship W2083095625A5022664058 @default.
• W2083095625 hasAuthorship W2083095625A5047496441 @default.
• W2083095625 hasAuthorship W2083095625A5056635728 @default.
• W2083095625 hasAuthorship W2083095625A5061087485 @default.
• W2083095625 hasConcept C106487976 @default.
• W2083095625 hasConcept C11413529 @default.
• W2083095625 hasConcept C114614502 @default.
• W2083095625 hasConcept C118615104 @default.
• W2083095625 hasConcept C121332964 @default.
• W2083095625 hasConcept C130367717 @default.
• W2083095625 hasConcept C147710293 @default.
• W2083095625 hasConcept C158693339 @default.
• W2083095625 hasConcept C159985019 @default.
• W2083095625 hasConcept C164226766 @default.
• W2083095625 hasConcept C187834632 @default.
• W2083095625 hasConcept C192562407 @default.
• W2083095625 hasConcept C202444582 @default.
• W2083095625 hasConcept C2524010 @default.
• W2083095625 hasConcept C28826006 @default.
• W2083095625 hasConcept C33923547 @default.
• W2083095625 hasConcept C62520636 @default.
• W2083095625 hasConcept C84545080 @default.
• W2083095625 hasConceptScore W2083095625C106487976 @default.
• W2083095625 hasConceptScore W2083095625C11413529 @default.
• W2083095625 hasConceptScore W2083095625C114614502 @default.
• W2083095625 hasConceptScore W2083095625C118615104 @default.
• W2083095625 hasConceptScore W2083095625C121332964 @default.
• W2083095625 hasConceptScore W2083095625C130367717 @default.
• W2083095625 hasConceptScore W2083095625C147710293 @default.
• W2083095625 hasConceptScore W2083095625C158693339 @default.
• W2083095625 hasConceptScore W2083095625C159985019 @default.
• W2083095625 hasConceptScore W2083095625C164226766 @default.
• W2083095625 hasConceptScore W2083095625C187834632 @default.
• W2083095625 hasConceptScore W2083095625C192562407 @default.
• W2083095625 hasConceptScore W2083095625C202444582 @default.
• W2083095625 hasConceptScore W2083095625C2524010 @default.
• W2083095625 hasConceptScore W2083095625C28826006 @default.
• W2083095625 hasConceptScore W2083095625C33923547 @default.
• W2083095625 hasConceptScore W2083095625C62520636 @default.
• W2083095625 hasConceptScore W2083095625C84545080 @default.
• W2083095625 hasIssue "1" @default.
• W2083095625 hasLocation W20830956251 @default.
• W2083095625 hasOpenAccess W2083095625 @default.
• W2083095625 hasPrimaryLocation W20830956251 @default.
• W2083095625 hasRelatedWork W2022265318 @default.

• next