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Modified block jacobi preconditioners for the conjugate gradient method, part i (1995).
| Content Provider | CiteSeerX |
|---|---|
| Author | Bollhöfer, M. He, C. Mehrmann, V. |
| Abstract | We discuss modified block Jacobi preconditioners for the conjugate gradient (CG) method to solve a linear system of equations Ax = b on a parallel computer. The new preconditioners are constructed to be close to an optimal block diagonal preconditioner of the form minC cond(C \Gamma1 A); but chosen so that Rank(A \Gamma C) is minimal and that the clustering of eigenvalues is improved. The construction of the preconditioner is based on the divide and conquer method for linear systems. Properties of these new preconditioners are discussed and some numerical examples are given to demonstrate that the CG method with one of the modified block Jacobi preconditioner is always faster than that with the standard block Jacobi preconditioner, but it is expensive to be constructed. When A satisfies a certain block-diagonally dominant condition, the same property is found to be true for another modified block Jacobi preconditioner which is easy to be constructed. 1 Introduction In this paper w... |
| File Format | |
| Publisher Date | 1995-01-01 |
| Access Restriction | Open |
| Subject Keyword | Modified Block Jacobi Preconditioners Conjugate Gradient Method New Preconditioners Modified Block Jacobi Preconditioner Linear System Optimal Block Diagonal Preconditioner Numerical Example Dominant Condition Standard Block Jacobi Preconditioner Equation Ax Conjugate Gradient Conquer Method Parallel Computer Form Minc Cond Cg Method |
| Content Type | Text |
| Resource Type | Article |
