Difference between revisions of "QR decomposition methods for dense Hessenberg matrices"
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| − | The '''QR decomposition of dense Hessenberg matrices''' arises as a part of one step of the [[ | + | The '''QR decomposition of dense Hessenberg matrices''' arises as a part of one step of the [[QR_algorithm|QR algorithm]]. However, in modern variants of the [[QR-алгоритм|QR algorithm]], this problem is solved implicitly using the fact that the product RQ must be calculated later at the same step, again in an implicit manner. Depending on the chosen shift strategy, one uses the implicit scheme with either a single shift or a double shift. The former is based on the Givens method, while the latter is based on the Householder method. |
[[Category:Finished articles]] | [[Category:Finished articles]] | ||
[[ru:Методы QR-разложения плотных хессенберговых матриц]] | [[ru:Методы QR-разложения плотных хессенберговых матриц]] | ||
Revision as of 17:08, 16 March 2018
The QR decomposition of dense Hessenberg matrices arises as a part of one step of the QR algorithm. However, in modern variants of the QR algorithm, this problem is solved implicitly using the fact that the product RQ must be calculated later at the same step, again in an implicit manner. Depending on the chosen shift strategy, one uses the implicit scheme with either a single shift or a double shift. The former is based on the Givens method, while the latter is based on the Householder method.
