On a computational method for the second fundamental tensor and its application to bifurcation problems

DOI10.1007/BF01386437zbMath0699.65037OpenAlexW1966795173MaRDI QIDQ913454

Werner C. Rheinboldt, Patrick J. Rabier

Publication date: 1990

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133475

zbMATH Keywords

algorithmJacobiannumerical examplessubmersionsecond fundamental tensorRiemannian submanifoldRiemann curvature tensorlocal iterative processmultiple bifurcation directionsprincipal cost

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Differential geometric aspects in vector and tensor analysis (53A45) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Numerical differentiation (65D25) Software, source code, etc. for problems pertaining to differential geometry (53-04)

Related Items (9)

On the local qualitative behavior of differential-algebraic equations ⋮ On the theory and error estimation of the reduced basis method for multi-parameter problems ⋮ Geometric notes on optimization with equality constraints ⋮ Optimization over geodesics for exact principal geodesic analysis ⋮ MANPAK: A set of algorithms for computations on implicitly defined manifolds ⋮ A homotopy method with adaptive basis selection for computing multiple solutions of differential equations ⋮ An adaptive homotopy method for computing bifurcations of nonlinear parametric systems ⋮ Numerical continuation methods: a perspective ⋮ Computing a closest bifurcation instability in multidimensional parameter space

Uses Software

• PITCON

Cites Work

• A generalization of the implicit function theorem for mappings from \({\mathcal R}^{n+1}\) into \({\mathcal R}^ n\) and its applications
• On the computation of multi-dimensional solution manifolds of parametrized equations
• On the Computation of Manifolds of Foldpoints for Parameter-Dependent Problems
• A locally parameterized continuation process
• A Geometric Framework for the Numerical Study of Singular Points
• Characterization and Computation of Singular Points with Maximum Rank Deficiency
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