## Approximate Inverse Preconditioners for General Sparse Matrices (1994)

Citations: | 25 - 6 self |

### BibTeX

@TECHREPORT{Chow94approximateinverse,

author = {Edmond Chow and Yousef Saad},

title = {Approximate Inverse Preconditioners for General Sparse Matrices},

institution = {},

year = {1994}

}

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### 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 \GammaAM k F , 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 each column to maintain sparsity in the approximate inverse. Compared to previous methods, this is a natural way to determine the sparsity pattern of the approximate inverse. This paper discusses options such as Newton and `global' iteration, self-preconditioning, dropping strategies, and factorized forms. The performance of the options are compared on standar...