Fast solving of Weighted Pairing Least-Squares systems

Details Fast solving of Weighted Pairing Least-Squares systems Fast solving of Weighted Pairing Least-Squares systems

2009-02-06

arxiv.org/abs/0902.1040v2

Journal of Computational and Applied Mathematics 231, 1 (2009) 39-48

Computer Science

Mathematical Software

Scientific paper

10.1016/j.cam.2009.01.016

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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