# Unitary triangularization of a nonsymmetric matrix

Abstract : 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...
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https://hal.archives-ouvertes.fr/hal-01316095
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### Citation

Alston Householder. Unitary triangularization of a nonsymmetric matrix. Journal of the ACM (JACM), Association for Computing Machinery, 1958, ⟨10.1145/320941.320947⟩. ⟨hal-01316095⟩

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