On a modification of the QZ algorithm with fast Givens rotations (Q1819540)
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scientific article; zbMATH DE number 3992792
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a modification of the QZ algorithm with fast Givens rotations |
scientific article; zbMATH DE number 3992792 |
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On a modification of the QZ algorithm with fast Givens rotations (English)
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1987
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It is explained, how Householder reflections can be replaced by fast Givens rotations in the first and second step of the QZ algorithm. A count of the required operations for the two steps shows, that the modified first step does need less operations, but that the modified second step needs only insigificantly less operations in comparison with the original QZ algorithm. On the base of this fact a modification of the second step is proposed. The resulting new algorithm is called FQZ algorithm, which has the same numerical properties as the QZ algorithm, if a correct scaling is applied.
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generalized unsymmetric algebraic eigenvalue problem
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rounding error
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Householder reflections
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fast Givens rotations
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QZ algorithm
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FQZ algorithm
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scaling
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0.8663224
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0.8568617
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0.8565345
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0.8418467
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0.8315825
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