References
- Hestenes , M. R. and Stiefel , E. 1952 . Methods of conjugate gradients for solving linear systems . Nat. Bureau Stand. J. Res. , 49 : 409 – 436 .
- Eisenstat , S. C. , Elman , H. C. and Schultz , M. H. 1983 . Variational iterative methods for nonsymmetric systems of linear equations . SI AM J. Numer. Anal. , 20 : 345 – 357 .
- Meijerink , J. A. and Van der Vorst , H. A. 1977 . An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix . Math. Comp. , 31 : 148 – 162 .
- Kershaw , D. S. 1978 . The incomplete Cholesky-Conjugate Gradient method for the iterative solution of systems of linear equations . J. Comp. Phys. , 26 : 43 – 65 .
- Gambolati , G. , Pini , G. and Zilli , G. 1988 . Numerical comparisons of preconditionings for large sparse finite element problems . Numerical Methods for Partial Differential Equations , 4 : 139 – 157 .
- Gambolati , G. , Pini , G. and Sartoretto , F. 1988 . An improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices . J. Comp. Phys. , 74 : 41 – 60 .
- Concus , P. and Golub , G. H. 1976 . “ A generalized conjugate gradient method for nonsymmetric systems of linear equations ” . In Lecture Notes in Economics and Mathematical System 134 , Edited by: Glowinski , R. and Lions , J. 56 – 65 . Berlin : Springer-Verlag .
- Saad , Y. and Schultz , M. H. 1986 . Conjugate algorithms for solving nonsymmetric linear systems . Math. of Comput. , 44 : 417 – 424 .
- Obeysekare , U. , Allen , M. , Ewing , R. and Jorge , J. 1987 . Application of conjugate-gradient-like methods to a hyperbolic problem in porous-media flow . Int. J. Num. Fluids , 7 : 551 – 566 .
- Vatsya , S. R. 1988 . Convergence of conjugate residual-like methods to solve linear equations . SIAM J. Numer. Anal. , 25 ( No. 4 ) : 957 – 364 .
- Pini , G. and Zilli , G. 1989 . Preconditioned iterative algorithms for large sparse unsymmetric problems . Numerical Methods for Partial Differential Equations , 5 ( No. 4 ) : 107 – 120 .
- Johnson , O. G. , Micchelli , C. A. and Paul , G. 1983 . Polynomial preconditioners for conjugate gradient calculations . SIAM J. Numer. Anal. , 20 ( No. 4 ) : 362 – 376 .
- Saad , Y. 1985 . Practical use of polynomial preconditionings for the conjugate gradient method . SIAM J. Sci. Stat. Comput. , 6 ( No. 4 ) : 865 – 881 .
- Vinsome , P. K. W. 1976 . Orthomin, an iterative method for solving sparse sets of simultaneous linear equations, Proc. 1976 . pp. 149 – 159 . Fourth Symposium on Reservoir Simulation, Soc. Pet. Eng. of AIME .
- van der Vorst , H. A. 1982 . A vectorizable variant of some ICCG methods . SI AM J. Sci. Stat. Comput. , 3 ( No. 3 ) : 350 – 356 .
- van der Vorst , H. A. 1986 . The performance of FORTRAN implementations for preconditioned conjugate gradients on vector computers . Parallel Computing , 3 ( No. 3 ) : 49 – 58 .
- Ashcraft , C. and Grimes , R. 1988 . On vectorizing incomplete factorization and SSOR preconditioners . SIAM J. Sci. Stat. Comput. , 8 ( No. 3 ) : 122 – 151 .
- Anderson , E. and Saad , Y. Solving sparse triangular linear systems on parallel computers . 1976 . Rome : Symposium on Vector and Parallel Processors for Scientific Computation—2 .
- Filippone , S. , Radicati di Brozolo , G. and Pini , G. 1988 . “ Vectorized ILU preconditioners for general sparsity patterns ” . In Proceedings of the International Meeting on Parallel Computing , Edited by: Evans , D. J. and Sutti , C. 103 – 114 . Bristol and Philadelphia : Adam Hilger .
- Pini G. Gambolati G. Is a simple diagonal scaling the best preconditioner for conjugate gradients on supercomputers Submitted to Advances in Water Resources
- Meyer , P. D. , Valocchi , A. J. , Ashby , S. F. and Saylor , P. E. in press . A numerical investigation of the conjugate gradient method as applied to three-dimensional groundwater flow problems in randomly heterogeneous porous media . Water Resour. Res., ,
- Peters , A. , Romunde , B. and Sartoretto , F. 1988 . Vectorized implementation of some MCG Codes for F. E. solution of large groundwater flow problems . Proceedings of the International Conference on Computational Methods in Flow Analysis . 1988 , Okayama, Japan.
- Lawson , C. L. , Hanson , R. J. , Kincaid , D. R. and Krogh , F. T. 1979 . Basic linear algebra subprograms for Fortran usage . ACM Trans. Math. Software , 5 : 308 – 323 .
- Kincaid D. R. Oppe T. C. Respess J. R. Young D. M. ITPACKV 2C User' s Guide Center for Numerical Analysis Univ. of Texas Austin 1984 Report CNA-191
- Galeati , G. , Gambolati , G. and Pini , G. “ Upwind preconditioned conjugate gradients for finite element transport models ” . In Proceedings of Groundwater contamination: Use of models in decision making, 285 – 299 .
- 1986b CRAY—FORTRAN (CFT), Reference Manual SR-0009, revision L-01
- 1984 CRAY—Library Reference Manual SR-0014, revision H