A Singular Value Homotopy for Finding Critical Parameter Values
Document Type
Article
Digital Object Identifier (DOI)
10.1016/j.apnum.2020.11.009
Journal Title
Applied Numerical Mathematics
Publication Date
3-2021
Abstract
Various applications in science and engineering depend upon computing real solutions to systems of analytic equations which depend upon real parameters. Locally in the parameter space, the qualitative behavior of the solutions remains the same except at critical parameter values. This article develops a singular value homotopy that aims to compute critical parameter values. Several examples are presented including computing critical parameter values for nonlinear boundary value problems, turning points for a steady-state system connected to learning and memory, and computing the maximum Gaussian curvature of a surface.
Publisher Statement
© 2020 published by Elsevier. This manuscript is made available under the Elsevier user license https://www.elsevier.com/open-access/userlicense/1.0/.
NOTE: Preprint submitted to Applied Numerical Mathematics.
Recommended Citation
Collins, J. B., and Jonathan D. Hauenstein. 2021. “A Singular Value Homotopy for Finding Critical Parameter Values.” Applied Numerical Mathematics 161 (March): 233–43. https://doi.org/10.1016/j.apnum.2020.11.009.
Comments
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