Abstract
In some previous papers the author extended two algorithms proposed by Z. Kovarik for approximate orthogonalization of a finite set of linearly independent vectors from a Hilbert space, to the case when the vectors are rows (not necessary linearly independent) of an arbitrary rectangular matrix. In this paper we describe combinations between these two methods and the classical Kaczmarz’s iteration. We prove that, in the case of a consistent least-squares problem, the new algorithms so obtained converge to any of its solutions (depending on the initial approximation). The numerical experiments described in the last section of the paper on a problem obtained after the discretization of a first kind integral equation ilustrate the fast convergence of the new algorithms.
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Popa, C. A fast Kaczmarz-Kovarik algorithm for consistent least-squares problems. Korean J. Comput. & Appl. Math. 8, 9–26 (2001). https://doi.org/10.1007/BF03011619
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DOI: https://doi.org/10.1007/BF03011619