Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 231, Issue 1, Pages 39-48Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2009.01.016
Keywords
Weighted pairing least-squares; Generalized inverses; Generalized Cholesky factor
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This paper presents a generalization of the weighted least-squares (WLS), named weighted pairing least-squares (WPLS), which uses a rectangular weight matrix and is suitable for data alignment problems. Two fast solving methods, suitable for solving full rank systems as well as rank deficient systems, are studied. Computational experiments clearly show that the best method, in terms of speed, accuracy, and numerical stability, is based on a special {1, 2, 3}-inverse, whose computation reduces to a very simple generalization of the usual Cholesky factorization-backward substitution method for solving linear systems. (C) 2009 Elsevier B.V. All rights reserved.
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