Continuation of Invariant Subspaces in Large Bifurcation Problems

DOI10.1137/060654219zbMath1160.65065OpenAlexW2029662995MaRDI QIDQ3617180

Mark J. Friedman, David Bindel, James W. Demmel

Publication date: 27 March 2009

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/060654219

zbMATH Keywords

algorithminvariant subspacesbifurcation analysiscontinuationRitz-Galerkin methodssmooth eigendecompositions

Mathematics Subject Classification ID

Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Computational methods for bifurcation problems in dynamical systems (37M20) Numerical bifurcation problems (65P30)

Related Items (14)

Degenerate Bogdanov-Takens bifurcations in a one-dimensional transport model of a fusion plasma ⋮ Evans function computation for the stability of travelling waves ⋮ Root Following in Evans Function Computation ⋮ Numerical computation of bifurcations in large equilibrium systems in \textsc{Matlab} ⋮ A bisection-like algorithm for branch switching at a simple branch point ⋮ Iterative refinement of Schur decompositions ⋮ Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values ⋮ First-Order Perturbation Theory for Eigenvalues and Eigenvectors ⋮ Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems ⋮ Refining estimates of invariant and deflating subspaces for large and sparse matrices and pencils ⋮ Grassmannian spectral shooting ⋮ Efficient computation of analytic bases in Evans function analysis of large systems ⋮ Projected nonsymmetric algebraic Riccati equations and refining estimates of invariant and deflating subspaces ⋮ Initialization of Homoclinic Solutions near Bogdanov--Takens Points: Lindstedt--Poincaré Compared with Regular Perturbation Method

Uses Software

• LAPACK
• MATCONT
• JDQR
• JDQZ

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