PREQN
Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method 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
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References in zbMATH (referenced in 9 articles , 1 standard article )
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Sorted by year (- Al-Baali, Mehiddin; Caliciotti, Andrea; Fasano, Giovanni; Roma, Massimo: A class of approximate inverse preconditioners based on Krylov-subspace methods for large-scale nonconvex optimization (2020)
- Fasano, Giovanni; Roma, Massimo: Preconditioning Newton-Krylov methods in nonconvex large scale optimization (2013)
- Alekseev, A. K.; Navon, I. M.; Steward, J. L.: Comparison of advanced large-scale minimization algorithms for the solution of inverse ill-posed problems (2009)
- Cullum, J. K.; Tůma, M.: Matrix-free preconditioning using partial matrix estimation (2006)
- Roma, Massimo: Dynamic scaling based preconditioning for truncated Newton methods in large scale unconstrained optimization (2005)
- Daescu, Dacian; Navon, I. M.: An analysis of a hybrid optimization method for variational data assimilation (2003)
- Fukuda, Mituhiro; Kojima, Masakazu; Shida, Masayuki: Lagrangian dual interior-point methods for semidefinite programs (2002)
- Morales, José Luis; Nocedal, Jorge: Enriched methods for large-scale unconstrained optimization (2002)
- Morales, José Luis; Nocedal, Jorge: Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method (2001)