Householder transformations revisited (Q2706238)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Householder transformations revisited |
scientific article |
Statements
19 March 2001
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Householder matrices
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elementary Hermitian matrices
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elementary reflectors
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rotators
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orthogonalization
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information carrier
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Householder reflections
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implicit QR algorithm
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eigenvalue
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Householder transformations
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Householder transformations revisited (English)
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There are two types of Householder reflections: One is the generally recommended, and the other was defined by \textit{B. N. Parlett} [SIAM Rev. 13, 197-208 (1971; Zbl 0217.52606)]. An important application of Householder reflectors is found in the implementation of the implicit QR algorithm for algebraic eigenvalue problem. In this paper, a new analysis of the two types of Householder reflections is presented. The results show that the second type defined by Parlett has a better ability to propagate information borne by its driving vector. This suggests that the two types of Householder transformations serve different purposes.
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