## Approximate Inverse Preconditioners Via Sparse-Sparse Iterations (1998)

Citations: | 78 - 17 self |

### BibTeX

@MISC{Chow98approximateinverse,

author = {Edmond Chow and YOUSEF SAAD},

title = {Approximate Inverse Preconditioners Via Sparse-Sparse Iterations},

year = {1998}

}

### Years of Citing Articles

### OpenURL

### Abstract

. The standard incomplete LU (ILU) preconditioners often fail for general sparse indefinite matrices because they give rise to `unstable' factors L and U . In such cases, it may be attractive to approximate the inverse of the matrix directly. This paper focuses on approximate inverse preconditioners based on minimizing kI \Gamma AMkF , where AM is the preconditioned matrix. An iterative descent-type method is used to approximate each column of the inverse. For this approach to be efficient, the iteration must be done in sparse mode, i.e., with `sparse-matrix by sparse-vector' operations. Numerical dropping is applied to maintain sparsity; compared to previous methods, this is a natural way to determine the sparsity pattern of the approximate inverse. This paper describes Newton, `global' and column-oriented algorithms, and discusses options for initial guesses, self-preconditioning, and dropping strategies. Some limited theoretical results on the properties and convergence of approxima...