Algorithm PREQN Fortran Subroutines for Preconditioning the Conjugate Gradient Method

PREQN is a package of Fortran subroutines for automatically generating pre conditioners for the conjugate gradient method It is designed for solving a sequence of linear systems Aix bi i t where the coe cient matrices Ai are symmetric and positive de nite and vary slowly Problems of this type arise for example in non linear 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 Aiv 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