Algorithm 809: PREQN
- 1 March 2001
- journal article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Mathematical Software
- Vol. 27 (1), 83-91
- https://doi.org/10.1145/382043.382343
Abstract
PREQN is a package of Fortran 77 subroutins for automatically generating preconditioners for the conjugate gradient method. It is designed for solving a sequence of linear systems A i x = b i , i = 1…, t , where the coefficient matrices A i are symmetric and positive definite and vary slowly. Problems of this type arise, for example, in nonlinear optimization. The preconditioners are based on limited-memory quasi-Newton updating and are recommended for problems in which (i) the coefficient matrices are not explicitly known and only matrix-vector products of the form A i v can be computed; or (ii) the coefficient matrices are not sparse. PREQN is written so that a single call from a conjugate gradient routine performs the preconditioning operation and stores information needed for the generation of a new preconditioner.Keywords
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