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Zbl 1053.65041
Reich, Simeon; Xu, Hong-Kun
An iterative approach to a constrained least squares problem. (English)
[J] Abstr. Appl. Anal. 2003, No. 8, 503-512 (2003). ISSN 1085-3375; ISSN 1687-0409/e

Summary: A constrained least squares problem in a Hilbert space $H$ is considered. The standard Tikhonov regularization method is used. In the case where the set of the constraints is the nonempty intersection of a finite collection of closed convex subsets of $H$, an iterative algorithm is designed. The resulting sequence is shown to converge strongly to the unique solution of the regularized problem. The net of the solutions to the regularized problems strongly converges to the minimum norm solution of the least squares problem if its solution set is nonempty.

MSC 2000:: *65J10 Equations with linear operators (numerical methods)
65J20 Improperly posed problems (numerical methods in abstract spaces)
47A52 Ill-posed problems etc.

Keywords: convergence; least squares problem; Hilbert space; Tikhonov regularization; iterative algorithm; minimum norm solution

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