Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method

PREQN is a package of Fortran 77 subroutines for automatically generating p reconditioners for the conjugate gradient method. It is designed for solvin g a sequence of linear systems A(i)x = bi, i = 1, ..., t, where the coeffic ient matrices Ai are symmetric and positive definite and vary slowly. Probl ems of this type arise, for example, in nonlinear optimization. The precond itioners are based on limited-memory quasi-Newton updating and are recommen ded for problems in which (i) the coefficient matrices are not explicitly k nown and only matrix-vector products of the form Aiv can be computed; or (i i) the coefficient matrices are not sparse. PREQN is written so that a sing le call from a conjugate gradient routine performs the preconditioning oper ation and stores information needed for the generation of a new preconditio ner.