This paper presents a digest of recently developed simplicial and continuation methods for approximating fixed-points or zero-points of nonlinear finite-dimensional mappings. Underlying the methods are algorithms for following curves which are implicitly defined, as for example, in the case of homotopies. The details of several algorithms are outlined sufficiently that they should be easily implemented. Applications of simplicial and continuation methods to nonlinear complementarily, location of critical points, location of multiple solutions and bifurcation are presented.
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%0 Journal Article
%1 allgower1980simplicial
%A Allgower, Eugene
%A Georg, Kurt
%D 1980
%J SIAM Review
%K 01a6-development-of-contemporary-mathematics 47h10-fixed-point-theorems 55m20-fixed-points-and-coincidences-in-algebraic-topology 65-02-numerical-analysis-research-exposition 65-03-history-of-numerical-analysis 65h10-systems-of-nonlinear-algebraic-equations 65j05-numerical-analysis-in-abstract-spaces 65k05-numerical-mathematical-programming-methods 90c25-convex-programming 90c33-complementarity-and-equilibrium-problems-and-variational-inequalities-finite-dimensions
%P 28-85
%R 10.1137/1022003
%T Simplicial and continuation methods for approximating fixed points and solutions to systems of equations
%U https://epubs.siam.org/doi/10.1137/1022003
%V 22
%X This paper presents a digest of recently developed simplicial and continuation methods for approximating fixed-points or zero-points of nonlinear finite-dimensional mappings. Underlying the methods are algorithms for following curves which are implicitly defined, as for example, in the case of homotopies. The details of several algorithms are outlined sufficiently that they should be easily implemented. Applications of simplicial and continuation methods to nonlinear complementarily, location of critical points, location of multiple solutions and bifurcation are presented.
@article{allgower1980simplicial,
abstract = {This paper presents a digest of recently developed simplicial and continuation methods for approximating fixed-points or zero-points of nonlinear finite-dimensional mappings. Underlying the methods are algorithms for following curves which are implicitly defined, as for example, in the case of homotopies. The details of several algorithms are outlined sufficiently that they should be easily implemented. Applications of simplicial and continuation methods to nonlinear complementarily, location of critical points, location of multiple solutions and bifurcation are presented.
},
added-at = {2023-11-06T23:48:16.000+0100},
author = {Allgower, Eugene and Georg, Kurt},
biburl = {https://www.bibsonomy.org/bibtex/2cedccbd992480d5a00cf9708be7bdbe6/gdmcbain},
doi = {10.1137/1022003},
interhash = {a023010db8bfb4e19769b1f6a65eeba4},
intrahash = {cedccbd992480d5a00cf9708be7bdbe6},
journal = {SIAM Review},
keywords = {01a6-development-of-contemporary-mathematics 47h10-fixed-point-theorems 55m20-fixed-points-and-coincidences-in-algebraic-topology 65-02-numerical-analysis-research-exposition 65-03-history-of-numerical-analysis 65h10-systems-of-nonlinear-algebraic-equations 65j05-numerical-analysis-in-abstract-spaces 65k05-numerical-mathematical-programming-methods 90c25-convex-programming 90c33-complementarity-and-equilibrium-problems-and-variational-inequalities-finite-dimensions},
pages = {28-85},
timestamp = {2023-11-07T00:34:58.000+0100},
title = {Simplicial and continuation methods for approximating fixed points and solutions to systems of equations},
url = {https://epubs.siam.org/doi/10.1137/1022003},
volume = 22,
year = 1980
}