Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F14%3A00432761" target="_blank" >RIV/67985807:_____/14:00432761 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1137/130931588" target="_blank" >http://dx.doi.org/10.1137/130931588</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/130931588" target="_blank" >10.1137/130931588</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

Popis výsledku v původním jazyce

New preconditioning strategies for solving m n overdetermined large and sparse linear least squares problems using the CGLS method are described. First, direct preconditioning of the normal equations by the Balanced Incomplete Factorization (BIF) for symmetric and positive definite matrices is studied and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU factors of an n n submatrix of the system matrix is our second approach. A new way to find this submatrix based ona specific weighted transversal problem is proposed. Numerical experiments demonstrate different algebraic and implementational features of the new approaches and put them into the context of current progress in preconditioning of CGLS. It is shown, in particular, that the robustness demonstrated earlier by the BIF preconditioning strategy transfers into the linear least squares solvers and the use of the weighted transversal helps to improve the LU-based approach.

Název v anglickém jazyce

Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

Popis výsledku anglicky

New preconditioning strategies for solving m n overdetermined large and sparse linear least squares problems using the CGLS method are described. First, direct preconditioning of the normal equations by the Balanced Incomplete Factorization (BIF) for symmetric and positive definite matrices is studied and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU factors of an n n submatrix of the system matrix is our second approach. A new way to find this submatrix based ona specific weighted transversal problem is proposed. Numerical experiments demonstrate different algebraic and implementational features of the new approaches and put them into the context of current progress in preconditioning of CGLS. It is shown, in particular, that the robustness demonstrated earlier by the BIF preconditioning strategy transfers into the linear least squares solvers and the use of the weighted transversal helps to improve the LU-based approach.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal on Scientific Computing

ISSN

1064-8275

e-ISSN

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Svazek periodika

36

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

"A2002"-"A2022"

Kód UT WoS článku

000344743800028

EID výsledku v databázi Scopus

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