19018707

Source:http://linkedlifedata.com/resource/pubmed/id/19018707

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Predicate	Object
rdf:type	pubmed:Citation
lifeskim:mentions	umls-concept:C0025663, umls-concept:C0086022, umls-concept:C0442335, umls-concept:C0542569, umls-concept:C1521738, umls-concept:C1705099
pubmed:issue	5
pubmed:dateCreated	2009-8-31
pubmed:abstractText	Newton's method for solving the matrix equation F(X) identical to AX-XX(T) AX = 0 runs up against the fact that its zeros are not isolated. This is due to a symmetry of F by the action of the orthogonal group. We show how differential-geometric techniques can be exploited to remove this symmetry and obtain a "geometric" Newton algorithm that finds the zeros of F. The geometric Newton method does not suffer from the degeneracy issue that stands in the way of the original Newton method.
pubmed:language	eng
pubmed:journal	http://linkedlifedata.com/resource/pubmed/journal/9426182
pubmed:citationSubset	IM
pubmed:status	MEDLINE
pubmed:month	May
pubmed:issn	0899-7667
pubmed:author	pubmed-author:AbsilP APA, pubmed-author:De LathauwerLL, pubmed-author:IshtevaMM, pubmed-author:Van HuffelSS
pubmed:issnType	Print
pubmed:volume	21
pubmed:owner	NLM
pubmed:authorsComplete	Y
pubmed:pagination	1415-33
pubmed:meshHeading	pubmed-meshheading:19018707-Algorithms, pubmed-meshheading:19018707-Artificial Intelligence, pubmed-meshheading:19018707-Computer Simulation, pubmed-meshheading:19018707-Humans, pubmed-meshheading:19018707-Signal Processing, Computer-Assisted
pubmed:year	2009
pubmed:articleTitle	A geometric Newton method for Oja's vector field.
pubmed:affiliation	Department of Mathematical Engineering, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium. absil@inma.ucl.ac.be
pubmed:publicationType	Journal Article, Research Support, Non-U.S. Gov't