Numerical methods for generalized least squares problems
Proceedings of the 6th international congress on Computational and applied mathematics
The generalized Cholesky factorization method for saddle point problems
Applied Mathematics and Computation
Robust image matching under partial occlusion and spatially varying illumination change
Computer Vision and Image Understanding - Special issue on robusst statistical techniques in image understanding
Straight monotonic embedding of data sets in Euclidean spaces
Neural Networks
Rounding error analysis of the classical Gram-Schmidt orthogonalization process
Numerische Mathematik
A weighted least squares method for scattered data fitting
Journal of Computational and Applied Mathematics
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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.