Givens method

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. Template:Шаблон:Матрица вращения 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. Various uses are possible for the QR decomposition of A. It can be used for solving a SLAE (System of Linear Algebraic Equations) Ax = b or as a step in the so-called QR algorithm for finding the eigenvalues of a matrix.