Premium
On the solution of indefinite systems arising in nonlinear programming problems
Author(s) -
Bonettini Silvia,
Ruggiero Valeria,
Tinti Federica
Publication year - 2007
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.558
Subject(s) - conjugate gradient method , mathematics , convergence (economics) , factorization , nonlinear system , linear system , nonlinear conjugate gradient method , nonlinear programming , mathematical optimization , conjugate residual method , derivation of the conjugate gradient method , numerical analysis , algorithm , computer science , mathematical analysis , gradient descent , physics , quantum mechanics , machine learning , artificial neural network , economics , economic growth
This work is concerned with the convergence properties and the numerical analysis of the preconditioned conjugate gradient (PCG) method applied to the solution of indefinite linear systems arising in nonlinear optimization. Our approach is based on the choice of quasidefinite preconditioners and of a suitable factorization routine. Some theoretical and numerical results about these preconditioners are obtained. Furthermore, we show the behaviour of the PCG method for different formulations of the indefinite system and we compare the effectiveness of the proposed variants. Copyright © 2007 John Wiley & Sons, Ltd.