Successive preconditioned conjugate gradient method for the minimization of quadratic and nonlinear functions

Applied Numerical Mathematics

Volumn 35, Issue 2, 2000, Pages 129-156

  Davey, K ^a   Ward, M J ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; MATRIX ALGEBRA; POLYNOMIALS; QUADRATIC PROGRAMMING;

HESSIAN MATRIX; PRECONDITIONED CONJUGATE GRADIENT METHODS; QUADRATIC POLYNOMIALS;

NONLINEAR EQUATIONS;

EID: 0034299715     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(99)00053-7     Document Type: Article

References (22)

1. O. Axelsson, A survey of preconditioned iterative methods for linear systems of equations, BIT 25 (1985) 166-187.
2. O. Axelsson, P.S. Vassilevski, A black box generalized conjugate gradient solver with inner iterations and variable-step preconditioning, SIAM J. Matrix Anal. Appl. 12 (1991) 625-644.
3. P. Concus, G.H. Golub, G. Meurant, Block preconditioning for the conjugate gradient method, SIAM J. Sci. Statist. Comput. 6 (1985) 220-252.
4. K. Davey, M.J. Ward, An efficient solution method for finite element ring rolling simulation, Internat. J. Numer. Methods Engrg. (1999) in press.
5. R. Dembo, S. Eisenstat, T. Steihaug, Inexact newton methods, SIAM J. Numer. Anal. 19 (1985) 400-408.
6. J.E. Dennis, Jr., J. Moré, Quasi-newton methods, motivation and theory, SIAM Rev. 19 (1977) 46-89.
7. T. Eirola, O. Nevanlinna, Accelerating with rank-one updates, Linear Algebra Appl. 121 (1989) 511-520.
8. S.C. Eisenstat, Efficient implementation of a class of preconditioned conjugate gradient methods, SIAM J. Sci. Statist. Comput. 2 (1984) 1-4.
9. A. George, On block elimination for sparse linear systems, SIAM J. Numer. Anal. 12 585-603.
10. P.E. Gill, W. Murray, Quasi-newton methods for unconstrained optimization, J. Inst. Math. Appl. 9 (1972) 99-108.
11. A. Greenbaum, Iterative methods for solving linear equations, Frontiers in Applied Mathematics, Vol. 17, SIAM, Philadelphia, PA, 1997.
12. M. Herrmann, K.M. Lange, A joint project to simulate metal forming processes, in: Chenot, Wood and Zienkiewicz (Eds.), NUMIFORM'92, Balkema, Rotterdam, 1992, pp. 255-260.
13. M.R. Hestenes, E. Stiefel, Methods of conjugate gradients for solving linear systems of equations, J. Res. Nat. Bur. Stand. 49 (1952) 409-436.
14. C.T. Kelly, Iterative methods for linear and nonlinear equations, Frontiers in Applied Mathematics, Vol. 16, SIAM, Philadelphia, PA, 1995.
15. D.S. Kershaw, The incomplete cholesky conjugate gradient method for the iterative solution of linear systems, J. Comput. Phys. 26 (1978) 43-65.
16. D.G. Luenberger, Introduction to Linear and Nonlinear Programming, Addison-Wesley, New York, 1973.
17. T.A. Manteuffel, An incomplete factorization technique for positive definite linear systems, Math. Comp. 34 (1980) 473-497.
18. J.K. Reid, On the method of conjugate gradients for the solution of large sparse systems of linear systems of linear equations, in: J.K. Reid (Ed.), Large Sparse Sets of Linear Equations, Academic Press, New York, 1971, pp. 231-254.
19. Y. Saad, A flexible inner-outer preconditioned GMRES algorithm, SIAM J. Sci. Statist. Comput. 14 (1993) 461-469.
20. L.E. Scales, Introduction to Nonlinear Optimization, MacMillan, London, 1985.
21. A. van der Sluis, H.A. van der Vorst, The rate of convergence of conjugate gradients, Numer. Math. 48 (1986) 543-560.
22. H.A. van der Vorst, C. Vuik, GMRESR: A family of nested GMRES methods, Numer. Linear Algebra Appl. 1 (1994) 369-386.