Solving nonlinear equations by adaptive homotopy continuation

DOI10.1016/0096-3003(91)90064-TzbMath0717.65031MaRDI QIDQ2638726

Yanyan Li

Publication date: 1991

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

systems of nonlinear equationscomplex parameterNumerical exampleshomotopy continuation methodscontinuation parameter

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20)

Related Items

Optimal homotopy methods for solving nonlinear systems. I: Nonsingular homotopy paths, On higher-order differentiation in nonlinear mechanics, Obtaining initial parameter estimates for nonlinear systems using multicriteria associative memories, Using monodromy to avoid high precision in homotopy continuation, An adaptive learning approach to the identification of structural and mechanical systems, Work by Robert Kalaba on automated sensitivity analysis, A TFC-based homotopy continuation algorithm with application to dynamics and control problems, Phase path tracing methods for solving the high order zeros of nonlinear systems, Structure variable homotopy methods for solving nonlinear systems

Uses Software

• HOMPACK

Cites Work

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• A finite algorithm for the exact evaluation of higher order partial derivatives of functions of many variables
• Finding the zeros of an analytic function
• A fixed point algorithm with economic applications
• Parameter identification by continuation methods
• Nonlocal automated sensitivity analysis
• Algorithm 652
• Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
• Complete comparative static differential equations
• Finding Zeroes of Maps: Homotopy Methods That are Constructive With Probability One