publication . Article . Other literature type . 1958

unitary triangularization of a nonsymmetric matrix

HOUSEHOLDER, Alston;
Open Access
  • Published: 01 Oct 1958 Journal: Journal of the ACM (JACM), volume 5, pages 339-342 (issn: 0004-5411, eissn: 1557-735X, Copyright policy)
  • Publisher: Association for Computing Machinery (ACM)
Abstract
International audience; A method for the inversion of a nonsymmetric matrix, due to J. W. Givens, has been in use at Oak Ridge National Laboratory and has proved to be highly stable numerically but to require a rather large number of arithmetic operations, including a total of $n(n-1)/2$ square roots. Strictly, the method achieves the triangularization of the matrix, after which any standard method may be employed for inverting the triangle. The triangular form is brought about by means of a sequence of $n(n-1)/2$ plane rotations, whose product is an orthogonal matrix. Each rotation requires the extraction of a square root...
Subjects
free text keywords: Control and Systems Engineering, Hardware and Architecture, Software, Artificial Intelligence, Information Systems, Square matrix, Matrix (mathematics), Square number, Mathematics, Combinatorics, Discrete mathematics, Unitary state, Square root of a 2 by 2 matrix, Square root, [MATH]Mathematics [math]

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