A Singular Value Homotopy for Finding Critical Parameter Values

Document Type


Digital Object Identifier (DOI)


Journal Title

Applied Numerical Mathematics

Publication Date



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.


NOTE: To access the complete document: Click the "View Open Manuscript" link at the top of the page.

This open manuscript is freely available on the Elsevier ScienceDirect website at: https://doi.org/10.1016/j.apnum.2020.11.009.

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.