Unitary Triangularization of a Nonsymmetric Matrix

@article{Householder1958UnitaryTO,
  title={Unitary Triangularization of a Nonsymmetric Matrix},
  author={A. Householder},
  journal={J. ACM},
  year={1958},
  volume={5},
  pages={339-342}
}
A method for the inversion of a nonsymmetric matrix has been in use at ORNL 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. This note points out that the same result can be obtained with fewer arithmetic operations, and, in particular, for inverting a square matrix of order N, at most 2(N-1) square roots are required. For N > 4, this is a savings of (N-4)(N-1)/4 square roots. (T.B.A.) 
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