Selected References
(links valid as of Fall 2006)
Books
- Iterative Methods for Sparse Linear Systems, Saad, SIAM, 2003
- Matrix Computations, Golub and Van Loan, John's Hopkins, 1989
- Scientific Computing, An Introduction with Parallel Computing, Golub and Ortega, Academic Press, 1993
Software
Online Resources
Various Papers
- Incomplete Cholesky Factorization with Sparsity
Pattern Modification, Wang, Gallivan and Bramley, 1993 (tests given to insure the existence of an incomplete cholesky factorization)
- BiCGstab(l): an Efficient and Surprisingly Stable Solver of Nonsymmetric Linear Equations, G.L.G. Sleijpen, D.R. Fokkema, H.A. van der Vorst, 1994 (the ksp method which yielded tremendous speedups on several problems)
- Hybrid Bi-Conjugate Gradient Methods for CFD Problems, Gerard L.G. Sleijpen, Henk A. van der Vorst, 1995.
- Newton-Krylov-Schwarz Methods for Richard's Equation, E. W. Jenkins, R. C. Berger, J. P. Hallberg, Stacy E. Howington, C. T. Kelley, Joseph H. Schmidt, Alan Stagg, M. D. Tocci, 1999.
- A Two-Level Aggregation-Based Newton-Krylov-Schwarz Method for Hydrology, E. W. Jenkins, R. C. Berger, J. P. Hallberg, S. E. Howington, C. T. Kelley, J. H. Schmidt, A. K. Stagg, and M. D. Tocci, 1999.
- Accelerated Inexact Newton Schemes for Large Systems of Nonlinear Equations, Diederik R. Fokkema, Gerard L.G. Sleijpen, Henk A. Van der Vorst, SIAM Journal on Scientific Computing, 1995.
- Preconditioning Implicit Methods for Coupled Physics Problems, David Keyes, Old Dominion University, SciDAC, 2003.
- Approximate and Incomplete Factorizations, Tony F. Chan, Henk A. Van Der Vorst, 1994
- Parallel Preconditioners Based Upon Domain Decomposition, Jimack, P K and Hodgson, D C, Parallel and Distributed Processing for Computational Mechanics: Systems and Tools, ed. B.H.V. Topping (Saxe-Coburg Publications), 1999.
- Algebraic Theory of Multiplicative Schwarz Methods, Michele Benzi, Andreas Frommer, Reinhard Nabben, and Daniel B. Szyld, Numerische Mathematik, 2001.
- Comparisions between multiplicative and additive schwarz iterations in domain decomposition methods, Reinhard Nabben, Numerische Mathematik 95, 145-162, 2003.
- Convergence theory of restricted multiplicative Schwarz methods , Reinhard Nabben and Daniel Szyld, SIAM Journal on Numerical Analysis, 2003.
- Optimal Left and Right Additive Schwarz Preconditioning for Minimal Residual Methods with Euclidean and Energy Norms, Marcus Sarkis and Daniel B. Szyld, 2006.(A theoretical justification for the practical use of Euclidean norm minimization methods preconditioned with additive schwarz.)