Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates (Q2780615)
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scientific article; zbMATH DE number 1729225
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates |
scientific article; zbMATH DE number 1729225 |
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15 April 2002
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principal angles
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canonical correlations
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subspaces
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scalar product
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orthogonal projection
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algorithm
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accuracy
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round-off errors
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perturbation analysis
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numerical results
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Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates (English)
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The authors formulate a sine and cosine based algorithm for computing the principal angles between subspaces that provide accurate computation of all principal angles. The algorithm is generalized to the computation of principal angles in an arbitrary \(A\)-based scalar product, where \(A\) is a symmetric, positive definite matrix.NEWLINENEWLINENEWLINEThe theoretical justification of the generalized algorithm is presented. Furthermore, perturbation estimates for absolute errors in sine and cosine of the principal angles are derived. The implementation of the proposed algorithm is discussed in detail. Finally, the robustness of the presented algorithm is demonstrated by numerical results.
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