2,896 research outputs found
Perturbation bounds for constrained and weighted least squares problems
AbstractWe derive perturbation bounds for the constrained and weighted linear least squares (LS) problems. Both the full rank and rank-deficient cases are considered. The analysis generalizes some results of earlier works
Fast solving of Weighted Pairing Least-Squares systems
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
Accurate computation of the Moore-Penrose inverse of strictly totally positive matrices
The computation of the Moore-Penrose inverse of structured strictly totally positive matrices is addressed. Since these matrices are usually very ill-conditioned, standard algorithms fail to provide accurate results. An algorithm based on the factorization and which takes advantage of the special structure and the totally positive character of these matrices is presented. The first stage of the algorithm consists of the accurate computation of the bidiagonal decomposition of the matrix. Numerical experiments illustrating the good behavior of our approach are included.Numerical experiments illustrating the good behavior of our approach are included
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