On neighbouring matrices with quadratic elementary divisors |
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| Authors: | J. H. Wilkinson |
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| Affiliation: | (1) Department of Computer Science, The University of Adelaide, G.P.O. Box 498, 5001 Adelaide, S.A., Australia;(2) Present address: Weapons Systems Research Laboratory, G.P.O. Box 2151, 5001 Adelaide, S.A., Australia |
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| Abstract: | Summary Algorithms are presented which compute theQR factorization of an order-n Toeplitz matrix inO(n2) operations. The first algorithm computes onlyR explicitly, and the second computes bothQ andR. The algorithms are derived from a well-known procedure for performing the rank-1 update ofQR factors, using the shift-invariance property of the Toeplitz matrix. The algorithms can be used to solve the Toeplitz least-squares problem, and can be modified to solve Toeplitz systems inO(n) space. |
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| Keywords: | AMS(MOS) Mathematical Reviews Classification: 65F Computing Reviews Classification: 5.1 |
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