Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method
ACM Transactions on Mathematical Software (TOMS)
Enriched Methods for Large-Scale Unconstrained Optimization
Computational Optimization and Applications
Parallel multiscale Gauss-Newton-Krylov methods for inverse wave propagation
Proceedings of the 2002 ACM/IEEE conference on Supercomputing
High Resolution Forward And Inverse Earthquake Modeling on Terascale Computers
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Preconditioner updates applied to CFD model problems
Applied Numerical Mathematics
Optimization Methods & Software
Improving Triangular Preconditioner Updates for Nonsymmetric Linear Systems
Large-Scale Scientific Computing
Nonsymmetric Preconditioner Updates in Newton-Krylov Methods for Nonlinear Systems
SIAM Journal on Scientific Computing
Low-rank update of preconditioners for the inexact Newton method with SPD Jacobian
Mathematical and Computer Modelling: An International Journal
Computational Optimization and Applications
GPText: Greenplum parallel statistical text analysis framework
Proceedings of the Second Workshop on Data Analytics in the Cloud
Preconditioning Newton---Krylov methods in nonconvex large scale optimization
Computational Optimization and Applications
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This paper proposes a preconditioner for the conjugate gradient method (CG) that is designed for solving systems of equations Ax=bi with different right-hand-side vectors or for solving a sequence of slowly varying systems Ak x = bk. The preconditioner has the form of a limited memory quasi-Newton matrix and is generated using information from the CG iteration. The automatic preconditioner does not require explicit knowledge of the coefficient matrix A and is therefore suitable for problems where only products of A times a vector can be computed. Numerical experiments indicate that the preconditioner has most to offer when these matrix-vector products are expensive to compute and when low accuracy in the solution is required. The effectiveness of the preconditioner is tested within a Hessian-free Newton method for optimization and by solving certain linear systems arising in finite element models.