The Equality Constrained Indefinite Least Squares Problem: Theory and Algorithms
| Autor: | Adam W. Bojanczyk, Nicholas J. Higham, Harikrishna Patel |
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| Rok vydání: | 2003 |
| Předmět: |
Numerical linear algebra
Computer Networks and Communications Applied Mathematics Numerical analysis computer.software_genre QR decomposition Algebra Computational Mathematics Non-linear least squares Orthogonal matrix Round-off error computer Algorithm Software Mathematics Numerical stability Cholesky decomposition |
| Zdroj: | BIT Numerical Mathematics. 43:505-517 |
| ISSN: | 0006-3835 |
| DOI: | 10.1023/b:bitn.0000007020.58972.07 |
| Popis: | We present theory and algorithms for the equality constrained indefinite least squares problem, which requires minimization of an indefinite quadratic form subject to a linear equality constraint. A generalized hyperbolic QR factorization is introduced and used in the derivation of perturbation bounds and to construct a numerical method. An alternative method is obtained by employing a generalized QR factorization in combination with a Cholesky factorization. Rounding error analysis is given to show that both methods have satisfactory numerical stability properties and numerical experiments are given for illustration. This work builds on recent work on the unconstrained indefinite least squares problem by Chandrasekaran, Gu, and Sayed and by the present authors. |
| Databáze: | OpenAIRE |
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