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Factorized Sparse Approximate Inverses for Preconditioning.

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Title: Factorized Sparse Approximate Inverses for Preconditioning.
Authors: Huckle, Thomas1 huckle@in.tum.de
Source: Journal of Supercomputing. Jun2003, Vol. 25 Issue 2, p109-117. 9p.
Subjects: Sparse matrix software, Sparse matrices, Matrices (Mathematics), Algorithms
Abstract: In recent papers the use of sparse approximate inverses for the preconditioning of linear equations Ax=b is examined. The minimization of ||AM-I|| in the Frobenius norm generates good preconditioners without any a priori knowledge on the pattern of M. For symmetric positive definite A and a given a priori pattern there exist methods for computing factorized sparse approximate inverses L with LLT≈A-;1. Here, we want to modify these algorithms that they are able to capture automatically a promising pattern for L. We use these approximate inverses for solving linear equations with the cg-method. Furthermore we introduce and test modifications of this method for computing factorized sparse approximate inverses. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Supercomputing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Factorized Sparse Approximate Inverses for Preconditioning.
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  Data: In recent papers the use of sparse approximate inverses for the preconditioning of linear equations Ax=b is examined. The minimization of ||AM-I|| in the Frobenius norm generates good preconditioners without any a priori knowledge on the pattern of M. For symmetric positive definite A and a given a priori pattern there exist methods for computing factorized sparse approximate inverses L with LLT≈A-;1. Here, we want to modify these algorithms that they are able to capture automatically a promising pattern for L. We use these approximate inverses for solving linear equations with the cg-method. Furthermore we introduce and test modifications of this method for computing factorized sparse approximate inverses. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Supercomputing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1023/A:1023988426844
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      – SubjectFull: Sparse matrices
        Type: general
      – SubjectFull: Matrices (Mathematics)
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      – SubjectFull: Algorithms
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      – TitleFull: Factorized Sparse Approximate Inverses for Preconditioning.
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              Text: Jun2003
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