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A singular value homotopy for finding critical parameter values. (English) Zbl 07310816
Summary: 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.
MSC:
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
Software:
Maple; AUTO; Bertini; MATCONT
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