New perturbation bounds and condition numbers for the hyperbolic QR factorization |
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Authors: | Hanyu Li Peng Lv |
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Affiliation: | 1. College of Mathematics and Statistics, Chongqing University, Chongqing, P.R. China.hyli@cqu.edu.cn;3. College of Mathematics and Statistics, Chongqing University, Chongqing, P.R. China. |
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Abstract: | Using the modified matrix-vector equation approach, the technique of Lyapunov majorant function and the Banach fixed point theorem, we obtain some new rigorous perturbation bounds for R factor of the hyperbolic QR factorization under normwise perturbation. These bounds are always tighter than the one given in the literature. Moreover, the optimal first-order perturbation bounds and the normwise condition numbers for the hyperbolic QR factorization are also presented. |
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Keywords: | Hyperbolic QR factorization Lyapunov majorant function Banach fixed point theorem rigorous perturbation bound condition number |
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