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Predictor-corrector and simplicial methods for approximating fixed points and zero points of nonlinear mappings. (English) Zbl 0541.65032

Mathematical programming, 11th int Symp., Bonn 1982, 15-56 (1983).
[For the entire collection see Zbl 0533.00035.]
This paper represents an introduction as well as a state of the art survey concerning homotopy methods for numerically approximating fixed points and zero-points of nonlinear mappings. Among the topics treated are: the construction of homotopies and conditions for attaining solutions; an outline of a predictor corrector algorithm for numerically tracing a homotopy path; an application to unconstrained optimization; an outline of a simplicial algorithm for tracing a homotopy path; and a simplicial algorithm using a refining triangulation. A bibliography with several hundred titles is included.

MSC:

65H10 Numerical computation of solutions to systems of equations
65K05 Numerical mathematical programming methods
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
90C30 Nonlinear programming

Citations:

Zbl 0533.00035

Software:

PLALGO