Introduction to Numerical Continuation Methods

By Eugene L. Allgower, Kurt Georg. 1987

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Citations in the corpus

Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques (2009, methodology): “In this study, the NNMs are determined using methods for the numerical continuation of periodic motions (also called path-following methods) [4,5,33].”
Factorized Graph Matching (2016, methodology): “guaranteed to converge to an integer one and therefore no rounding step is needed; (3) The iteratively updating procedure resembles the idea of numerical continuation methods [60], which have been used for solving nonlinear systems of equations for decades.”
NEUROECONOMICS: A CRITICAL RECONSIDERATION (2008, background): “Allgower and Georg (2003) draw a distinction between two types of ways in which one can follow a homotopy path.”
Post-bifurcation and stability of a finitely strained hexagonal honeycomb subjected to equi-biaxial in-plane loading (2016, unknown): “The complete numerical characterization of such an equilibrium manifold requires the use of multi-parameter continuation methods ( Allgower and Georg, 2003 ).”
Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples (2017, unknown): “To follow this branch numerically would require specific pathfollowing techniques, [7].”
Curriculum Learning: A Survey (2021, methodology): “Research on continuation methods is therefore considered an independent field of study (Allgower and Georg 2003; Chow et al. 1991), not necessarily bound to its applications in machine learning (Richter and DeCarlo 1983), as would be the case for curriculum learning.”
Piecewise polynomial chaos expansion with an application to brake squeal of a linear brake system (2013, methodology): “Second method: Continuation Another point of view is to consider that the sought values are continuous from one cell to another and hence, to apply some continuations principles (see [43] for the continuation methods).”
Winning the Lottery with Continuous Sparsification (2019, methodology): “The core of our method lies in constructing a smooth continuation path [20] connecting training of soft-gated parameters and the intractable `0-regularized objective.”
Adaptively Localized Continuation-Newton Method—Nonlinear Solvers That Converge All the Time (2010, methodology): “In order to overcome this challenge, we design a numerical continuation algorithm (Allgower and Georg 1980, 2003; Shroff and Keller 1993; Watson et al. 1987) that proceeds from the initial state from which the solution path emanates.”
T-snakes: Topology adaptive snakes (2000, background): “It arbitrary point (x, y) by bilinearly interpolating the intenupdates the positions of the model nodes from time t to sities at the four pixels surrounding (x, y).”