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Preconditioning methods for linear systems arising in constrained optimization problems
Author(s) -
Axelsson Owe,
Neytcheva Maya
Publication year - 2002
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.310
Subject(s) - preconditioner , saddle point , mathematics , eigenvalues and eigenvectors , saddle , factorization , linear system , interior point method , matrix (chemical analysis) , optimization problem , mathematical optimization , mathematical analysis , algorithm , geometry , physics , materials science , quantum mechanics , composite material
Preconditioning methods for matrices on saddle point form, as typically arising in equality constrained optimization problems, are surveyed. Special consideration is given to two methods: a nearly symmetric block incomplete factorization preconditioning method and a preconditioner on the same saddle point form as the given matrix. Both methods result in eigenvalues with positive real parts and small or zero imaginary parts. The behaviour of the methods are illustrated by solving a regularized Stokes problem. Copyright © 2002 John Wiley & Sons, Ltd.