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Zbl 0769.65026
Eicke, Bertolt
Iteration methods for convexly constrained ill-posed problems in Hilbert space.
(English)
[J] Numer. Funct. Anal. Optimization 13, No.5-6, 413-429 (1992). ISSN 0163-0563; ISSN 1532-2467/e

The author deals with minimizing a quadratic objective functional $f \to \Vert Af - g\Vert\sp 2$ over a closed convex constraint set $C$, where $A$ is a bounded linear operator. When the minimum is not unique, the author's suggestion is to look for the solution of minimal norm. In case the problem is ill-posed, i.e. the solution does not depend continuously on the data, then the problem can be solved by means of the Tikhonov- Phillips iterative regularization method.\par The regularities of three iterative methods, which are the projected Landweber iteration, the method of smooth solutions, and the damped projected Landweber iteration, are the main issue of this paper. Finally, the author applies these methods to specific problems and gives numerical results.
[Yu Wenhuan (Tianjin)]
MSC 2000:
*65J10 Equations with linear operators (numerical methods)
65J20 Improperly posed problems (numerical methods in abstract spaces)
47A50 Equations and inequalities involving linear operators

Keywords: ill-posed problem; convex constraints; solution of minimal norm; Tikhonov-Phillips iterative regularization method; Landweber iteration

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