Preconditioning of linear least squares by robust incomplete factorization for implicitly held normal equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10331039" target="_blank" >RIV/00216208:11320/16:10331039 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/16M105890X" target="_blank" >http://dx.doi.org/10.1137/16M105890X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/16M105890X" target="_blank" >10.1137/16M105890X</a>

Result language
angličtina
Original language name
Preconditioning of linear least squares by robust incomplete factorization for implicitly held normal equations
Original language description
The ecient solution of the normal equations corresponding to a large sparse linear least squares problem can be extremely challenging. Robust incomplete factorization (RIF) preconditioners represent one approach that has the important feature of computing an incomplete LLT factorization of the normal equations matrix without having to form the normal matrix itself. The right-looking implementation of Benzi and Tuma has been used in a number of studies but experience has shown that in some cases it can be computationally slow and its memory requirements are not known a priori. Here a new left-looking variant is presented that employs a symbolic preprocessing step to replace the potentially expensive searching through entries of the normal matrix. This involves a directed acyclic graph (DAG) that is computed as the computation proceeds. An inexpensive but eective pruning algorithm is proposed to limit the number of edges in the DAG. Problems arising from practical applications are used to compare the performance of the right-looking approach with a left-looking implementation that computes the normal matrix explicitly and our new implicit DAG-based left-looking variant.
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/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>
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
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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