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.
On the solution of indefinite systems arising in nonlinear programming problems / Bonettini, S.; Ruggiero, V.; Tinti, F.. - In: NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS. - ISSN 1070-5325. - 14:10(2007), pp. 807-831. [10.1002/nla.558]
On the solution of indefinite systems arising in nonlinear programming problems
Bonettini S.
;
2007
Abstract
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.
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