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2016•Unpublished venueRequires access

Convergence Acceleration of Iterative Methods for Inverting Real Matrices Using Frobenius Norm Minimization

Ajinkya Borle, Samuel J. Lomonaco

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Abstract

The Schulz-type methods for computing generalized matrix inverses are a family of iterative methods that are popular for their high order of convergence (≥ 2). We propose two new scaled acceleration techniques for such type of iterative methods for real matrices (based on Frobenius norm minimization) and lay out efficient algorithms to implement these techniques. Test results show one of our techniques to be most effective for dense matrices but also works for sparse cases as well.

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What this paper is about

The Schulz-type methods for computing generalized matrix inverses are a family of iterative methods that are popular for their high order of convergence (≥ 2). We propose two new scaled acceleration techniques for such type of iterative methods for real matrices (based on Frobenius norm minimization) and lay out efficient algorithms to implement these techniques. Test results show one of our techniques to be most effective for dense matrices but also works for sparse cases as well.

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Available abstract

The Schulz-type methods for computing generalized matrix inverses are a family of iterative methods that are popular for their high order of convergence (≥ 2). We propose two new scaled acceleration techniques for such type of iterative methods for real matrices (based on Frobenius norm minimization) and lay out efficient algorithms to implement these techniques. Test results show one of our techniques to be most effective for dense matrices but also works for sparse cases as well.

Key concepts: Matrix norm, Convergence (economics), Acceleration, Iterative method, Minification, Norm (philosophy), Matrix (chemical analysis), Computer science

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