Solution Methods for Large Sparse Linear Systems.
Final technical rept.,
ACADEMIC COMPUTER CENTER UTRECHT (NETHERLANDS)
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The discretisation of partial differential equations, by either finite element or finite difference techniques, often leads to large linear systems of equations with sparse matrices. Fast iterative solution methods, based upon the preconditioning of the conjugate gradients method, have been proposed for the symmetric positive definite case and also for more general situations. In this report we present new sharp upperbounds for the conjugate gradients residual. These upperbounds help us to understand and explain the convergence behaviour of the preconditioned conjugate gradients method. We also present a type of preconditioning that has almost the same convergence properties as those presented, but which admit- full vectorization on supercomputers like the CRAY-1 and the CYBER 205. For the nonsymmetric case we propose different types of preconditioning in connection with the Chebyshev iterative method. Author
- Numerical Mathematics