Allgower, E. L.; Georg, K. 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. Cited in 18 Documents 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 Keywords:survey; homotopy methods; fixed points; zero-points; predictor corrector algorithm; homotopy path; simplicial algorithm; refining triangulation; bibliography Citations:Zbl 0533.00035 Software:PLALGO PDFBibTeX XML