An improved incomplete Cholesky factorization
ACM Transactions on Mathematical Software (TOMS)
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Automatic Preconditioning by Limited Memory Quasi-Newton Updating
SIAM Journal on Optimization
Efficient Implementation of the Truncated-Newton Algorithm for Large-Scale Chemistry Applications
SIAM Journal on Optimization
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Enriched Methods for Large-Scale Unconstrained Optimization
Computational Optimization and Applications
Optimization Methods & Software
Preconditioning Newton---Krylov methods in nonconvex large scale optimization
Computational Optimization and Applications
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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 Aix = bi, i = 1…, t, where the coefficient matrices Ai 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 Aiv 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.