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Algorithm PREQN: Fortran 77 Subroutines for Preconditioning the Conjugate Gradient Method

By Jose Luis Morales and Jorge Nocedal


PREQN is a package of Fortran 77 subroutines for automatically generating preconditioners for the conjugate gradient method. It is designed for solving a sequence of linear systems A ix = b i � i =1�:::�t, where the coe cient matrices A i are symmetric and positive de nite 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 coe cient matrices are not explicitly known and only matrix-vector products of the form A iv can be computed� or ii) the coe cient 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

Topics: Additional Key Words and Phrases, Preconditioning, conjugate gradient method, quasi- Newton method, Hessian-free Newton method, limited memory method
Year: 2000
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