A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10386785" target="_blank" >RIV/00216208:11320/18:10386785 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11075-018-0478-2" target="_blank" >https://doi.org/10.1007/s11075-018-0478-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11075-018-0478-2" target="_blank" >10.1007/s11075-018-0478-2</a>

Result language
angličtina
Original language name
A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows
Original language description
The effectiveness of sparse matrix techniques for directly solving large-scale linear least-squares problems is severely limited if the system matrix A has one or more nearly dense rows. In this paper, we partition the rows of A into sparse rows and dense rows (A(s) and A(d)) and apply the Schur complement approach. A potential difficulty is that the reduced normal matrix A(s)(T) A(s) is often rank-deficient, even if A is of full rank. To overcome this, we propose explicitly removing null columns of A(s) and then employing a regularization parameter and using the resulting Cholesky factors as a preconditioner for an iterative solver applied to the symmetric indefinite reduced augmented system. We consider complete factorizations as well as incomplete Cholesky factorizations of the shifted reduced normal matrix. Numerical experiments are performed on a range of large least-squares problems arising from practical applications. These demonstrate the effectiveness of the proposed approach when combined with either a sparse parallel direct solver or a robust incomplete Cholesky factorization algorithm.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GC17-04150J" target="_blank" >GC17-04150J: Reliable two-scale Fourier/finite element-based simulations: Error-control, model reduction, and stochastics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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