We give a new characterization of the solutions set of the general (inconsistent) linear least-squares problem using the set of limit-points of an extended version of the classical Kaczmarz’s projections method. We also obtain a “ step error reduction formula” which, in some cases, can give us apriori information about the convergence properties of the algorithm. Some numerical experiments with our algorithm and comparisons between it and others existent in the literature, are made in the last section of the paper.
R. Radhakrishna and S.K. Mitra,Generalized inverse of matrices and its applications, John Willey and sons Inc., New York, 1971.MATHGoogle Scholar
N. Shinozaki, M. Sibuya, and K. Tanabe,Numerical methods for the Moore- Penrose inverse of a matrix, Annals of the Institute of Statistical Mathematics, 24(1972), 193–203 and 621–629.CrossRefMathSciNetGoogle Scholar
K. Tanabe,Conjugate gradient method for computing the Moore-Penrose inverse and rank of a matrix, Journal of Optimization Theory and Applications, 22(1)(1977), 1–23.MATHCrossRefMathSciNetGoogle Scholar
D.M. Young,Iterative solution of large linear systems, Academic Press, New York, 1971.MATHGoogle Scholar