Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
8-2016
Committee Chair or Co-Chairs
Jeff Knisley
Committee Members
Ariel Cintron-Arias, Robert Gardner
Abstract
Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R3, but also to the general case of finding minimal functionals on hypersurfaces in Rn associated with an arbitrary metric.
Document Type
Thesis - unrestricted
Recommended Citation
Whitinger, Robert, "An Algorithm for the Machine Calculation of Minimal Paths" (2016). Electronic Theses and Dissertations. Paper 3119. https://dc.etsu.edu/etd/3119
Copyright
Copyright by Robert Whitinger
Included in
Analysis Commons, Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons, Other Mathematics Commons, Partial Differential Equations Commons, Theory and Algorithms Commons