Krylov Subspace Iteration

Computing in Science and Engineering

Volumn 2, Issue 1, 2000, Pages 32-37

  Van Der Vorst, Henk A ^a,b  

^a Centre for Mathematics and Informatics   (Netherlands)

^b UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002912235     PISSN: 15219615     EISSN: None     Source Type: Journal    
DOI: 10.1109/5992.814655     Document Type: Review

References (11)

1. E. Bodewig, Matrix Calculus, North-Holland, Amsterdam, 1956.
2. D. Young, Iterative Solution of Large Linear Systems, Academic Press, San Diego, 1971.
3. D.M. Young, Iterative Methods for Solving Partial Differential Equations of Elliptic Type, doctoral thesis, Harvard Univ., Cambridge, Mass., 1950.
4. R.S. Varga, Matrix Iterative Analysis, Prentice-Hall, Upper Saddle River, N.J., 1962.
5. C. Lanczos, "Solution of Systems of Linear Equations by Minimized Iterations",J. Research Nat'l Bureau of Standards, Vol. 49, 1952, pp. 33-53.
6. W.E. Arnoldi, "The Principle of Minimized Iteration in the Solution of the Matrix Eigenproblem," Quarterly Applied Mathematics, Vol. 9, 1951, pp. 17-29.
7. M.R. Hestenes and E. Stiefel, "Methods of Conjugate Gradients for Solving Linear Systems," J. Research Nat'l Bureau of Standards, Vol. 49, 1954, pp. 409-436.
8. J.K. Reid, "The Use of Conjugate Gradients for Systems of Equations Possessing 'Property A,'" SIAM J. Numerical Analysis, Vol. 9, 1972, pp. 325-332.
9. D.S. Kershaw, "The Incomplete Choleski-Conjugate Gradient Method for the Iterative Solution of Systems of Linear Equations." J. Computational Physics, Vol. 26, No. 1, 1978, pp. 43-65.
10. Y. Saad and M.H. Schultz, "GMRES: A Generalized Minimal Residual Algorithm for Solving Nnonsymmetric Linear Systems," SIAM J. Scientific and Statistical Computing, Vol. 7, No. 3, 1986, pp. 856-869.
11. H.A. van der Vorst, "Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems," SIAM J. Scientific and Statistical Computing, Vol. 13, No. 2, 1992, pp. 631-644.