Difference between revisions of "Givens method"
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| − | '''Givens' method''' (which is also called '''the rotation method''' in the Russian mathematical literature) is used to represent a matrix in the form A = QR, where Q is a unitary and R is an upper triangular matrix. The matrix Q is not stored and used in its explicit form but rather as the product of rotations. Each (Givens) rotation can be specified by a pair of indices and a single parameter. In a conventional implementation of Givens' method | + | '''Givens' method''' (which is also called '''the rotation method''' in the Russian mathematical literature) is used to represent a matrix in the form ''A = QR'', where ''Q'' is a unitary and ''R'' is an upper triangular matrix. The matrix Q is not stored and used in its explicit form but rather as the product of rotations. Each (Givens) rotation can be specified by a pair of indices and a single parameter. In a conventional implementation of Givens' method, this fact makes it possible to avoid using additional arrays by storing the results of decomposition in the array originally occupied by ''A''. |
Revision as of 19:04, 21 January 2016
Primary authors of this description: A.V.Frolov, Vad.V.Voevodin (Section 2.2)
1 Properties and structure of the algorithm[edit]
1.1 General description of the algorithm
Givens' method (which is also called the rotation method in the Russian mathematical literature) is used to represent a matrix in the form A = QR, where Q is a unitary and R is an upper triangular matrix. The matrix Q is not stored and used in its explicit form but rather as the product of rotations. Each (Givens) rotation can be specified by a pair of indices and a single parameter. In a conventional implementation of Givens' method, this fact makes it possible to avoid using additional arrays by storing the results of decomposition in the array originally occupied by A.
