Engineering applications of the Chow-Yorke algorithm
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TLDR
The Chow-Yorke algorithm as discussed by the authors is a scheme for developing homotopy methods that are globally convergent with probability one, which has been successfully applied to a wide range of engineering problems, particularly those for which quasi-Newton and locally convergent iterative techniques are inadequate.About:
This article is published in Applied Mathematics and Computation.The article was published on 1981-09-01 and is currently open access. It has received 56 citations till now. The article focuses on the topics: Local convergence & Nonlinear complementarity problem.read more
Citations
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Introduction to Numerical Continuation Methods
Eugene L. Allgower,Kurt Georg +1 more
TL;DR: The Numerical Continuation Methods for Nonlinear Systems of Equations (NCME) as discussed by the authors is an excellent introduction to numerical continuuation methods for solving nonlinear systems of equations.
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Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms
TL;DR: HOMPACK provides three qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation-based, normal flow, and augmented Jacobian matrix.
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Continuation and path following
Eugene L. Allgower,Kurt Georg +1 more
TL;DR: The main ideas of path following by predictor–corrector and piecewise-linear methods, and their application in the direction of homotopy methods and nonlinear eigenvalue problems are reviewed.
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Artificial parameter homotopy methods for the DC operating point problem
TL;DR: The application of globally convergent probability-one homotopy methods to various systems of nonlinear equations that arise in circuit simulation is discussed and the theoretical claims of global convergence for such methods are substantiated.
References
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Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
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Quasi-Newton Methods, Motivation and Theory
John E. Dennis,Jorge J. Moré +1 more
TL;DR: In this paper, an attempt to motivate and justify quasi-Newton methods as useful modifications of Newton''s method for general and gradient nonlinear systems of equations is made, and references are given to ample numerical justification; here we give an overview of many of the important theoretical results.
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