Computing multiple turning points by using simple extended systems and computational differentiation

DOI10.1080/10556789908805731zbMath0929.65029OpenAlexW1985087558MaRDI QIDQ4254663

Hubert Schwetlick, Uwe Schnabel, Gerd Poenisch

Publication date: 11 January 2000

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556789908805731

zbMATH Keywords

Newton's methodsingular pointscomputational differentiationminimally extended systemsparametrized nonlinear equationsmultiple turning points

Mathematics Subject Classification ID

Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Uses Software

• ADOL-C

Cites Work

• Numerical computation of nonsimple turning points and cusps
• Singularities and groups in bifurcation theory. Volume I
• Bifurcation: analysis, algorithms, applications. Proceedings of the Conference at the University of Dortmund, August 18-22, 1986
• Computation of cusp singularities for operator equations and their discretizations
• Computing turning points of curves implicitly defined by nonlinear equations depending on a parameter
• A comparison of methods for determining turning points of nonlinear equations
• Computing multiple pitchfork bifurcation points
• Computing hysteresis points of nonlinear equations depending on two parameters
• Characterization and Computation of Generalized Turning Points
• Non-simple Turning Points and Cusps
• A direct method for the determination of non-simple turning points
• Minimally extended defining conditions for singularities of codim≤2
• A Method for the Numerical Determination of Bifurcation States of Nonlinear Systems of Equations
• Computation of Singularities in Large Nonlinear Systems
• Algorithm 755: ADOL-C
• Computational differentiation: techniques, applications, and tools

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