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.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etd-4521 |
| Date | 01 August 2016 |
| Creators | Whitinger, Robert |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses and Dissertations |
| Rights | Copyright by Robert Whitinger |
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