Abstract
In the past decade various complementary pivoting algorithms have been developed to search for fixed points of certain functions and point to set maps. All these methods generate a sequence of simplexes which are ‘shrinking’ to a point. This paper proposes a new method for shrinking the simplexes. It is shown that under certain conditions, the function whose fixed point is sought may be used to control this shrinking process. A computational method for implementing these ideas is also suggested and several examples are solved using this approach.
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An abstract appears in the November, 1978 issue of Notices of the American Mathematical Society.
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Solow, D. Homeomorphisms of triangulations with applications to computing fixed points. Mathematical Programming 20, 213–224 (1981). https://doi.org/10.1007/BF01589346
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DOI: https://doi.org/10.1007/BF01589346