This dissertation discusses a new approach to spline approximation. A periodic spline approximation 𝑓<sub>M,m,N</sub>(x) = Σ<sub>k=1</sub><sup>N</sup>α<sub>k</sub>Φ<sub>M,k</sub>(x) to a periodic function 𝑓(x) is determined by requiring < Φ<sub>m,j</sub>, 𝑓 - 𝑓<sub>M,m,N</sub> > = 0 for j = 1,...,N, where the Φ<sub>L,k</sub>'s are the unique periodic spline basis functions of order 𝐿. Error estimates, examples and some relationships to wavelets are given for the case M - m = 2μ. The case M - m = 2µ + 1 is briefly discussed but not completely explored. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/37448 |
| Date | 02 March 2006 |
| Creators | Bonawitz, Elizabeth Ann |
| Contributors | Mathematics, Russell, David L., Johnson, Lee W., Rogers, Robert C., Kohler, Werner E., Sun, Shu-Ming |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | viii, 112 leaves, BTD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 30932840, LD5655.V856_1994.B663.pdf |
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