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Journal Articles Journal of Computational and Applied Mathematics Year : 2009

Fast solving of Weighted Pairing Least-Squares systems

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1
Pierre Courrieu

Abstract

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.
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Dates and versions

hal-00358125 , version 1 (02-02-2009)
hal-00358125 , version 2 (29-05-2009)

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Pierre Courrieu. Fast solving of Weighted Pairing Least-Squares systems. Journal of Computational and Applied Mathematics, 2009, 231 (1), pp.39-48. ⟨10.1016/j.cam.2009.01.016⟩. ⟨hal-00358125v2⟩

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CNRS UNIV-AMU LPC
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