Inversion of analytic matrix functions that are singular at the origin (Q2719192)
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scientific article; zbMATH DE number 1608856
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inversion of analytic matrix functions that are singular at the origin |
scientific article; zbMATH DE number 1608856 |
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21 June 2001
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matrix inversion
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matrix valued functions
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analytic perturbation
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Laurent series
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algorithms
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symbolic algebra
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0.92732006
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0.9240772
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0.90988964
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0.9096856
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0.9002799
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0.8994063
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0.89913803
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Inversion of analytic matrix functions that are singular at the origin (English)
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Let \(z\mapsto A(z)= A_0+z A_1+\cdots\) be an analytic \(n\times n\) matrix valued function, defined in a neighbourhood of the origin. It is supposed that \(A_0\) is singular but \(A(z)\) is not for small \(z\neq 0\). Then there exists an integer \(s\geq 1\) such that \(A^{-1}(z)=z^{-s} (X_0+zX_1+\cdots)\). The authors discuss three computational procedures for determining the matrix coefficients \(X_k\), \(k=0,1, \dots\). A comparison is made with algorithms based on symbolic algebra.
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