An iterative method for linear discrete ill-posed problems with box constraints

Authors:
S. Morigi;L. Reichel;F. Sgallari;F. Zama
Affiliations:
Department of Mathematics, University of Bologna, Bologna, Italy;Department of Mathematical Sciences, Kent State University, Kent, OH;Department of Mathematics, University of Bologna, Bologna, Italy;Department of Mathematics, University of Bologna, Bologna, Italy
Venue:
Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
Year:
2007

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Abstract

Many questions in science and engineering give rise to linear discrete ill-posed problems. Often it is desirable that the computed approximate solution satisfies certain constraints, e.g., that some or all elements of the computed solution be nonnegative. This paper describes an iterative method of active set-type for the solution of large-scale problems of this kind. The method employs conjugate gradient iteration with a stopping criterion based on the discrepancy principle and allows updates of the active set by more than one index at a time.