SOLVING MIXED SPARSE-DENSE LINEAR LEAST-SQUARES PROBLEMS BY PRECONDITIONED ITERATIVE METHODS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10369987" target="_blank" >RIV/00216208:11320/17:10369987 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/16M1108339" target="_blank" >http://dx.doi.org/10.1137/16M1108339</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/16M1108339" target="_blank" >10.1137/16M1108339</a>

Result language
angličtina
Original language name
SOLVING MIXED SPARSE-DENSE LINEAR LEAST-SQUARES PROBLEMS BY PRECONDITIONED ITERATIVE METHODS
Original language description
The efficient solution of large linear least-squares problems in which the system matrix A contains rows with very different densities is challenging. Previous work has focused on direct methods for problems in which A has a few relatively dense rows. These rows are initially ignored, a factorization of the sparse part is computed using a sparse direct solver, and then the solution is updated to take account of the omitted dense rows. In some practical applications the number of dense rows can be significant, and for very large problems, using a direct solver may not be feasible. We propose processing rows that are identified as dense separately within a conjugate gradient method using an incomplete factorization preconditioner combined with the factorization of a dense matrix of size equal to the number of dense rows. Numerical experiments on large-scale problems from real applications are used to illustrate the effectiveness of our approach. The results demonstrate that we can efficiently solve problems that could not be solved by a preconditioned conjugate gradient method without exploiting the dense rows.
Czech name
—
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
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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