| dc.contributor.advisor | Ward, Joseph D. | |
| dc.creator | Hinrichs, Lisa Ninette | |
| dc.date.accessioned | 2022-06-30T16:00:10Z | |
| dc.date.available | 2022-06-30T16:00:10Z | |
| dc.date.issued | 1978 | |
| dc.identifier.uri | https://hdl.handle.net/1969.1/CAPSTONE-HinrichsL_1978 | |
| dc.description | Program year: 1977-1978 | en |
| dc.description | Digitized from print original stored in HDR | en |
| dc.description.abstract | Mathematicians use divided difference equations to solve problems which have only a discrete set of possible values. This research is concerned with the application of difference equations to curve fitting data by means of splines. There is a paper written by four math professors at Texas A&M which concerns itself with this data fitting problem. In particular, a theorem in this paper states conditions for when a complex data function has a unique best fit from a spline space. Central to the proof of this theorem was the necessity of deciding when certain determinants were positive using divided difference equations. The purpose of my research was to broaden the classes of matrices for which the determinant is positive which, in turn, would broaden the classes of functions for which one could obtain a unique piecewise spline. | en |
| dc.format.extent | 44 pages | en |
| dc.format.medium | electronic | en |
| dc.format.mimetype | application/pdf | |
| dc.subject | divided difference equations | en |
| dc.subject | splines | en |
| dc.subject | data fitting | en |
| dc.subject | complex data function | en |
| dc.subject | classes of matrices | en |
| dc.title | The Calculus of Finite Differences | en |
| dc.type | Thesis | en |
| thesis.degree.department | Mathematics | en |
| thesis.degree.grantor | University Undergraduate Fellows | en |
| thesis.degree.level | Undergraduate | en |
| dc.type.material | text | en |
