Matches in SemOpenAlex for { <https://semopenalex.org/work/W2141992912> ?p ?o ?g. }
Showing items 1 to 97 of
97
with 100 items per page.
- W2141992912 endingPage "658" @default.
- W2141992912 startingPage "625" @default.
- W2141992912 abstract "Abstract The QR algorithm is one of the classical methods to compute the eigendecomposition of a matrix. If it is applied on a dense n × n matrix, this algorithm requires O ( n 3 ) operations per iteration step. To reduce this complexity for a symmetric matrix to O ( n ), the original matrix is first reduced to tridiagonal form using orthogonal similarity transformations. In the report ( Report TW360 , May 2003) a reduction from a symmetric matrix into a similar semiseparable one is described. In this paper a QR algorithm to compute the eigenvalues of semiseparable matrices is designed where each iteration step requires O ( n ) operations. Hence, combined with the reduction to semiseparable form, the eigenvalues of symmetric matrices can be computed via intermediate semiseparable matrices, instead of tridiagonal ones. The eigenvectors of the intermediate semiseparable matrix will be computed by applying inverse iteration to this matrix. This will be achieved by using an O ( n ) system solver, for semiseparable matrices. A combination of the previous steps leads to an algorithm for computing the eigenvalue decompositions of semiseparable matrices. Combined with the reduction of a symmetric matrix towards semiseparable form, this algorithm can also be used to calculate the eigenvalue decomposition of symmetric matrices. The presented algorithm has the same order of complexity as the tridiagonal approach, but has larger lower order terms. Numerical experiments illustrate the complexity and the numerical accuracy of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd." @default.
- W2141992912 created "2016-06-24" @default.
- W2141992912 creator A5036811999 @default.
- W2141992912 creator A5039999347 @default.
- W2141992912 creator A5052654029 @default.
- W2141992912 date "2005-03-07" @default.
- W2141992912 modified "2023-10-13" @default.
- W2141992912 title "An implicitQR algorithm for symmetric semiseparable matrices" @default.
- W2141992912 cites W183455853 @default.
- W2141992912 cites W1964080902 @default.
- W2141992912 cites W1964799071 @default.
- W2141992912 cites W1973445645 @default.
- W2141992912 cites W1974473583 @default.
- W2141992912 cites W1976310561 @default.
- W2141992912 cites W1976676253 @default.
- W2141992912 cites W1999651301 @default.
- W2141992912 cites W2002864633 @default.
- W2141992912 cites W2014445436 @default.
- W2141992912 cites W2029837479 @default.
- W2141992912 cites W2054188927 @default.
- W2141992912 cites W2063561814 @default.
- W2141992912 cites W2069044345 @default.
- W2141992912 cites W2078464328 @default.
- W2141992912 cites W2145140212 @default.
- W2141992912 cites W2151757774 @default.
- W2141992912 cites W2160803104 @default.
- W2141992912 cites W2166268267 @default.
- W2141992912 cites W2170013390 @default.
- W2141992912 cites W266430444 @default.
- W2141992912 cites W4205764228 @default.
- W2141992912 cites W4292027041 @default.
- W2141992912 cites W608773355 @default.
- W2141992912 cites W614920821 @default.
- W2141992912 doi "https://doi.org/10.1002/nla.425" @default.
- W2141992912 hasPublicationYear "2005" @default.
- W2141992912 type Work @default.
- W2141992912 sameAs 2141992912 @default.
- W2141992912 citedByCount "38" @default.
- W2141992912 countsByYear W21419929122012 @default.
- W2141992912 countsByYear W21419929122013 @default.
- W2141992912 countsByYear W21419929122014 @default.
- W2141992912 countsByYear W21419929122016 @default.
- W2141992912 countsByYear W21419929122017 @default.
- W2141992912 countsByYear W21419929122022 @default.
- W2141992912 crossrefType "journal-article" @default.
- W2141992912 hasAuthorship W2141992912A5036811999 @default.
- W2141992912 hasAuthorship W2141992912A5039999347 @default.
- W2141992912 hasAuthorship W2141992912A5052654029 @default.
- W2141992912 hasBestOaLocation W21419929122 @default.
- W2141992912 hasConcept C106487976 @default.
- W2141992912 hasConcept C111335779 @default.
- W2141992912 hasConcept C11413529 @default.
- W2141992912 hasConcept C121332964 @default.
- W2141992912 hasConcept C158693339 @default.
- W2141992912 hasConcept C159985019 @default.
- W2141992912 hasConcept C188060507 @default.
- W2141992912 hasConcept C192562407 @default.
- W2141992912 hasConcept C207467116 @default.
- W2141992912 hasConcept C2524010 @default.
- W2141992912 hasConcept C33923547 @default.
- W2141992912 hasConcept C51647924 @default.
- W2141992912 hasConcept C62520636 @default.
- W2141992912 hasConceptScore W2141992912C106487976 @default.
- W2141992912 hasConceptScore W2141992912C111335779 @default.
- W2141992912 hasConceptScore W2141992912C11413529 @default.
- W2141992912 hasConceptScore W2141992912C121332964 @default.
- W2141992912 hasConceptScore W2141992912C158693339 @default.
- W2141992912 hasConceptScore W2141992912C159985019 @default.
- W2141992912 hasConceptScore W2141992912C188060507 @default.
- W2141992912 hasConceptScore W2141992912C192562407 @default.
- W2141992912 hasConceptScore W2141992912C207467116 @default.
- W2141992912 hasConceptScore W2141992912C2524010 @default.
- W2141992912 hasConceptScore W2141992912C33923547 @default.
- W2141992912 hasConceptScore W2141992912C51647924 @default.
- W2141992912 hasConceptScore W2141992912C62520636 @default.
- W2141992912 hasIssue "7" @default.
- W2141992912 hasLocation W21419929121 @default.
- W2141992912 hasLocation W21419929122 @default.
- W2141992912 hasOpenAccess W2141992912 @default.
- W2141992912 hasPrimaryLocation W21419929121 @default.
- W2141992912 hasRelatedWork W1980786482 @default.
- W2141992912 hasRelatedWork W2052778973 @default.
- W2141992912 hasRelatedWork W2353849135 @default.
- W2141992912 hasRelatedWork W2360550119 @default.
- W2141992912 hasRelatedWork W2389963024 @default.
- W2141992912 hasRelatedWork W3096021259 @default.
- W2141992912 hasRelatedWork W3165035967 @default.
- W2141992912 hasRelatedWork W3177208105 @default.
- W2141992912 hasRelatedWork W4212973497 @default.
- W2141992912 hasRelatedWork W748093718 @default.
- W2141992912 hasVolume "12" @default.
- W2141992912 isParatext "false" @default.
- W2141992912 isRetracted "false" @default.
- W2141992912 magId "2141992912" @default.
- W2141992912 workType "article" @default.