About: Conjugate residual method

An Entity of Type: Thing, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

The conjugate residual method is an iterative numeric method used for solving systems of linear equations. It's a Krylov subspace method very similar to the much more popular conjugate gradient method, with similar construction and convergence properties. This method is used to solve linear equations of the form where A is an invertible and Hermitian matrix, and b is nonzero. Given an (arbitrary) initial estimate of the solution , the method is outlined below: Note: the above algorithm can be transformed so to make only one symmetric matrix-vector multiplication in each iteration.

Property Value
dbo:abstract
  • The conjugate residual method is an iterative numeric method used for solving systems of linear equations. It's a Krylov subspace method very similar to the much more popular conjugate gradient method, with similar construction and convergence properties. This method is used to solve linear equations of the form where A is an invertible and Hermitian matrix, and b is nonzero. The conjugate residual method differs from the closely related conjugate gradient method primarily in that it involves more numerical operations and requires more storage, but the system matrix is only required to be Hermitian, not Hermitian positive definite. Given an (arbitrary) initial estimate of the solution , the method is outlined below: the iteration may be stopped once has been deemed converged. The only difference between this and the conjugate gradient method is the calculation of and (plus the optional incremental calculation of at the end). Note: the above algorithm can be transformed so to make only one symmetric matrix-vector multiplication in each iteration. (en)
dbo:wikiPageID
  • 29450651 (xsd:integer)
dbo:wikiPageLength
  • 3484 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1116626604 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dcterms:subject
rdfs:comment
  • The conjugate residual method is an iterative numeric method used for solving systems of linear equations. It's a Krylov subspace method very similar to the much more popular conjugate gradient method, with similar construction and convergence properties. This method is used to solve linear equations of the form where A is an invertible and Hermitian matrix, and b is nonzero. Given an (arbitrary) initial estimate of the solution , the method is outlined below: Note: the above algorithm can be transformed so to make only one symmetric matrix-vector multiplication in each iteration. (en)
rdfs:label
  • Conjugate residual method (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageDisambiguates of
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License