The multishift QR algorithm. II: Aggressive early deflation (Q2784390)
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scientific article; zbMATH DE number 1732281
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The multishift QR algorithm. II: Aggressive early deflation |
scientific article; zbMATH DE number 1732281 |
Statements
23 April 2002
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eigenvalues
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deflation
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implicit shifts
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convergence
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performance
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multishift QR algorithm
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The multishift QR algorithm. II: Aggressive early deflation (English)
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[For part I see ibid. 23, No. 4, 929-947 (2002; reviewed above).]NEWLINENEWLINENEWLINEfIn this second part, the authors enhance the performance of the multishift \(QR\) algorithm by adopting an aggressive early deflation, which takes advantage of matrix perturbations outside the subdiagonal entries of the Hessenberg \(QR\) iterates. It identifies and deflates the converged eigenvalues long before the classical small-subdiagonal strategy would and is particularly effective in combination with the small bulge multishift \(QR\) algorithm. This maintains a high rate of execution of floating point operations while significantly reducing the number of operations required.
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