Complete orthogonal decomposition for weighted least squares (1997) [11 citations — 3 self]
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@ARTICLE{Hough97completeorthogonal,author = {Patricia D. Hough and Stephen A. Vavasis},
title = {Complete orthogonal decomposition for weighted least squares},
journal = {SIAM J. Matrix Anal. Appl},
year = {1997},
volume = {18},
pages = {369--392}
}
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Abstract:
Consider a full-rank weighted least-squares problem in which the weight matrix is highly ill-conditioned. Because of the ill-conditioning, standard methods for solving least-squares problems, QR factorization and the nullspace method for example, break down. G. W. Stewart established a norm bound for such a system of equations, indicating that it may be possible to find an algorithm that gives an accurate solution. S. A. Vavasis proposed a new definition of stability that is based on this result. He also defined the NSH algorithm for solving this least-squares problem and showed that it satisfies his definition of stability. In this paper, we propose a complete orthogonal decomposition algorithm to solve this problem and show that it is also stable. This new algorithm is simpler and more efficient than the NSH method. 1
