On the Conditioning of Factors in the SR Decomposition
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F16%3A00456732" target="_blank" >RIV/67985807:_____/16:00456732 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.laa.2016.04.038" target="_blank" >http://dx.doi.org/10.1016/j.laa.2016.04.038</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2016.04.038" target="_blank" >10.1016/j.laa.2016.04.038</a>
Alternative languages
Result language
angličtina
Original language name
On the Conditioning of Factors in the SR Decomposition
Original language description
Almost every nonsingular matrix can be decomposed into the product of a symplectic matrix and an upper J-triangular matrix. This decomposition is not unique. In this paper we analyze the freedom of choice in the symplectic and the upper J-triangular factors and review several existing suggestions on how to choose the free parameters in the SR decomposition. In particula we consider two choices leading to the minimization of the condition number of the diagonal blocks in the upper J-triangular factor and to the minimization of the conditioning of the corresponding blocks in the symplectic factor. We develop bounds for the extremal singular values of the whole upper J-triangular factor and the whole symplectic factor in terms of the spectral properties of even-dimensioned principal submatrices of the skew-symmetric matrix associated with the SR decomposition. The theoretical results are illustrated on a small illustrative example.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA13-06684S" target="_blank" >GA13-06684S: Iterative Methods in Computational Mathematics: Analysis, Preconditioning, and Applications</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear Algebra and Its Applications
ISSN
0024-3795
e-ISSN
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Volume of the periodical
505
Issue of the periodical within the volume
15 September
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
224-244
UT code for WoS article
000378464500013
EID of the result in the Scopus database
2-s2.0-84966714537