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• W80502015 abstract "This chapter discusses some inherent properties of the paths generated by the recently developed methods used to solve numerically for fixed points of continuous mappings. These methods usually set up a homotopy between a simple problem that is easily solved, and the problem of interest, and then follow the path of fixed points of this homotopy. Under certain global conditions on the mapping, it can be shown that the path thus generated converges to a fixed point of the problem at hand. There are essentially two fundamental methods for following this path. The earlier method, called the simplicial approach, replaces this homotopy by a piece-wise linear approximation and follows the path of fixed points of this approximation. An approximate solution is then usually guaranteed under a standard existence theorem, such as the Brouwer fixed point theorem or the Leray-Schauder fixed point theorem. A residual subset of a topological space is a countable intersection of open dense subsets." @default.
• W80502015 created "2016-06-24" @default.
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• W80502015 date "1980-01-01" @default.
• W80502015 modified "2023-09-23" @default.
• W80502015 title "Some Generic Properties of Paths Generated by Fixed Point Algorithms" @default.
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• W80502015 doi "https://doi.org/10.1016/b978-0-12-590240-3.50007-0" @default.
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