BAND GENERALIZATION OF THE GOLUB-KAHAN BIDIAGONALIZATION, GENERALIZED JACOBI MATRICES, AND THE CORE PROBLEM

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10315163" target="_blank" >RIV/00216208:11320/15:10315163 - isvavai.cz</a>
Alternative codes found
RIV/67985807:_____/15:00446564 RIV/46747885:24510/15:#0001238 RIV/46747885:24510/15:00003941
Result on the web
<a href="http://dx.doi.org/10.1137/140968914" target="_blank" >http://dx.doi.org/10.1137/140968914</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/140968914" target="_blank" >10.1137/140968914</a>

Result language
angličtina
Original language name
BAND GENERALIZATION OF THE GOLUB-KAHAN BIDIAGONALIZATION, GENERALIZED JACOBI MATRICES, AND THE CORE PROBLEM
Original language description
The concept of the core problem in total least squares (TLS) problems with single right-hand side introduced in [C. C. Paige and Z. Strakos, SIAM J. Matrix Anal. Appl., 27 (2005), pp. 861-875] separates necessary and sufficient information for solving the problem from redundancies and irrelevant information contained in the data. It is based on orthogonal transformations such that the resulting problem decomposes into two independent parts. One of the parts has nonzero right-hand side and minimal dimensions and it always has the unique TLS solution. The other part has trivial (zero) right-hand side and maximal dimensions. Assuming exact arithmetic, the core problem can be obtained by the Golub-Kahan bidiagonalization. Extension of the core concept to the multiple right-hand sides case AX approximate to B in [I. Hnetynkova, M. Plesinger, and Z. Strakos, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 917-931], which is highly nontrivial, is based on application of the singular value decompos
Czech name
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Czech description
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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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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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