Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method

ACM Transactions on Mathematical Software

Volumn 27, Issue 1, 2001, Pages 83-91

  Morales, José Luis ^a   Nocedal, Jorge ^b  

^a INSTITUTO TECNOLÓGICO AUTÓNOMO DE MÉXICO   (Mexico)

^b NORTHWESTERN UNIVERSITY   (United States)

Author keywords

G.1.3 Numerical Analysis : Numerical linear algebra Linear systems (direct and iterative methods); G.1.6 Numerical Analysis : Optimization Gradient methods; Unconstrained optimization

Indexed keywords

EID: 0011630080     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/382043.382343     Document Type: Article

References (12)

1. CHAN, T. F. AND NG, M. K. 1996. Galerkin projection methods for solving multiple linear systems. 96-31. University of California at Los Angeles, Los Angeles, CA.
2. DENNIS, J. E. AND SCHNABEL, R. B. 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Inc., Upper Saddle River, NJ.
3. GREENBAUM, A. 1997. Iterative Methods for Solving Linear Systems. SIAM Frontiers in Applied Mathematics Series. SIAM, Philadelphia, PA.
4. JONES, M. T. AND PLASSMANN, P. E. 1995. An improved incomplete Cholesky factorization. ACM Trans. Math. Softw. 21, 1 (Mar.), 5-17.
5. MORALES, J. L. AND NOCEDAL, J. 2000. Automatic preconditioning by limited memory quasi-Newton updating. SIAM J. Optim. 10, 1079-1096.
6. NASH, S. G. 1984. Newton-type minimization via the Lanczos method. SIAM J. Numer. Anal. 21, 553-572.
7. NOCEDAL, J. 1980. Updating quasi-Newton matrices with limited storage. Math. Comput. 35, 773-782.
8. O'LEARY, D. P. 1982. A discrete Newton algorithm for minimizing a function of many variables. Math. Program. 23, 1, 20-33.
9. ORTEGA, J. M. AND RHEINBOLDT, W. C. 1970. Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, Inc., New York, NY.
10. STEIHAUG, T. 1983. The conjugate gradient method and trust regions in large scale optimization. SIAM J. Numer. Anal. 20, 626-637.
11. TOINT, P. L. 1981. Towards an efficient sparsity exploiting Newton method for minimization. In Sparse Matrices and Their Uses, I. S. Duff, Ed. Academic Press, Inc., New York, NY, 57-87.
12. XIE, D. AND SCHLICK, T. 2000. The truncated Newton search direction: Indefinite preconditioners and chemistry applications. SIAM J. Optim. 10, 132-154.