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- W2950616952 abstract "In this paper, we concentrate on the backward error and condition number of the indefinite least squares problem. For the normwise backward error of the indefinite least square problem, we adopt the linearization method to derive the tight estimations for the exact normwise backward errors. Using the dual techniques of condition number theory cite{22.0}, we derive the explicit expressions of the mixed and componentwise condition numbers for the linear function of the solution for the indefinite least squares problem. The tight upper bounds for the derived mixed and componentwise condition numbers are obtained, which can be estimated efficiently by means of the classical power method for estimating matrix 1-norm cite[Chapter 15]{Higham2002Book} during using the QR-Cholesky method cite{1.0} for solving the indefinite least squares problem. The numerical examples show that the derived condition numbers can give sharp perturbation bound with respect to the interested component of the solution. And the linearization estimations are effective for the normwise backward errors." @default.
- W2950616952 created "2019-06-27" @default.
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- W2950616952 date "2016-12-20" @default.
- W2950616952 modified "2023-09-30" @default.
- W2950616952 title "Backward error and condition number analysis for the indefinite linear least squares problem" @default.
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- W2950616952 doi "https://doi.org/10.48550/arxiv.1612.06655" @default.
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