Abstract
A family of iterative algorithms is presented for the solution of the symmetric linear complementarity problem,
whereM is a givenn×n symmetric real nonnegative matrix andq is a given positiven×1 vector. The algorithms are derived from a nonlinear relaxation method first proposed by Gold and Scofield for solving linear systems that arise from the discretization of certain linear integral equations. It is shown that the original algorithm has been used in several different fields of application like deconvolution, atmospheric sciences, computer graphics and image processing, and image reconstruction from projections. Convergence proofs are given.
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Communicated by O. L. Mangasarian
The research for this paper was supported by NIH Grant No. HL-28438.
We are grateful to Dr. Y. Censor for bringing Refs. 3, 4, 6, 7, 8 to our attention and to Ms. M. A. Blue for typing.
This paper was written while the author was an Invited Lecturer at the Medical Image Processing Group, Department of Radiology, Hospital of the University of Pennsylvania, Philadelphia, Pennsylvania.
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De Pierro, A.R. Nonlinear relaxation methods for solving symmetric linear complementarity problems. J Optim Theory Appl 64, 87–99 (1990). https://doi.org/10.1007/BF00940024
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DOI: https://doi.org/10.1007/BF00940024