Name
Title | ||
|---|---|---|
Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1145/382043.382343 | ACM Trans. Math. Softw. |
Keywords | Field | DocType |
coefficient matrix,form aiv,nonlinear optimization,matrix-vector product,limited-memory quasi-newton,hessian-free newton method,limited-memory method,new preconditioner,conjugate gradient method,conjugate gradient routine,preconditioning,linear system,quasi-newton method,coefficient matrices ai,quasi newton method,newton method,positive definite,conjugate gradient | Conjugate gradient method,Mathematical optimization,Quasi-Newton method,Preconditioner,Matrix (mathematics),Positive-definite matrix,Algorithm,Nonlinear conjugate gradient method,Mathematics,Conjugate residual method,Derivation of the conjugate gradient method | Journal |
Volume | Issue | ISSN |
27 | 1 | 0098-3500 |
Citations | PageRank | References |
7 | 0.63 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| José Luis Morales | 1 | 172 | 12.51 |
| Jorge Nocedal | 2 | 3276 | 301.50 |