PREQN swMATH ID: 1233 Software Authors: Morales, José Luis; Nocedal, Jorge Description: 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 Homepage: http://www.eecs.northwestern.edu/~nocedal/preqn.html Related Software: tn; L-BFGS; mctoolbox; KELLEY; CUTEr; TNPACK; MINRES; CUTEst; MINRES-QLP; Harwell-Boeing sparse matrix collection; HSL; SifDec; Algorithm 500; CG_DESCENT; SparseMatrix; ParaSails; ILUT; chammp; ARPACK; COL Cited in: 9 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method. Zbl 1070.65538Morales, José Luis; Nocedal, Jorge 2001 all top 5 Cited by 15 Authors 3 Roma, Massimo 2 Fasano, Giovanni 2 Morales, José Luis 2 Navon, Ionel Michael 2 Nocedal, Jorge 1 Al-Baali, Mehiddin 1 Alekseev, Aleksey K. 1 Caliciotti, Andrea 1 Cullum, Jane K. 1 Daescu, Dacian N. 1 Fukuda, Mituhiro 1 Kojima, Masakazu 1 Shida, Masayuki 1 Steward, J. L. 1 Tůma, Miroslav all top 5 Cited in 6 Serials 2 SIAM Journal on Optimization 2 Computational Optimization and Applications 2 Optimization Methods & Software 1 ACM Transactions on Mathematical Software 1 BIT 1 International Journal of Computational Fluid Dynamics Cited in 5 Fields 6 Numerical analysis (65-XX) 6 Operations research, mathematical programming (90-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Operator theory (47-XX) 1 Fluid mechanics (76-XX) Citations by Year