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- W49593721 abstract "In the last chapter we discussed the general features of PL continuation methods. In this chapter we will apply them to find a zero point of a map G : R N → R N . We will see that it is possible to greatly relax the smoothness hypotheses regarding the map G, which are usually assumed for numerically solving such problems. In fact, the map G may even be set-valued. Eaves (1971) showed that it is possible to calculate by PL algorithms the fixed points which are guaranteed to exist by a theorem of Kakutani (1941). Merrill (1972) gave a more general boundary condition for set-valued maps G, which is similar to the Leray-Schauder condition (11.2.12). In this chapter we present two PL algorithms due to Merrill (1972) and Eaves & Saigal (1972) which can be regarded as PL implementations of the homotopy method which was sketched generally in section 11.2. To insure success of the algorithms, we will follow a presentation of Georg (1982) which used a quite general boundary condition extending somewhat that used by Merrill." @default.
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- W49593721 date "1990-01-01" @default.
- W49593721 modified "2023-09-25" @default.
- W49593721 title "PL Homotopy Algorithms" @default.
- W49593721 doi "https://doi.org/10.1007/978-3-642-61257-2_13" @default.
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