A duality approach to spline approximation
| dc.contributor.author | Bonawitz, Elizabeth Ann | en |
| dc.contributor.committeechair | Russell, David L. | en |
| dc.contributor.committeemember | Johnson, Lee W. | en |
| dc.contributor.committeemember | Rogers, Robert C. | en |
| dc.contributor.committeemember | Kohler, Werner E. | en |
| dc.contributor.committeemember | Sun, Shu-Ming | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2014-03-14T21:09:54Z | en |
| dc.date.adate | 2006-03-02 | en |
| dc.date.available | 2014-03-14T21:09:54Z | en |
| dc.date.issued | 1994-04-21 | en |
| dc.date.rdate | 2006-03-02 | en |
| dc.date.sdate | 2006-03-02 | en |
| dc.description.abstract | 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. | en |
| dc.description.degree | Ph. D. | en |
| dc.format.extent | viii, 112 leaves | en |
| dc.format.medium | BTD | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.other | etd-03022006-093404 | en |
| dc.identifier.sourceurl | http://scholar.lib.vt.edu/theses/available/etd-03022006-093404/ | en |
| dc.identifier.uri | http://hdl.handle.net/10919/37448 | en |
| dc.language.iso | en | en |
| dc.publisher | Virginia Tech | en |
| dc.relation.haspart | LD5655.V856_1994.B663.pdf | en |
| dc.relation.isformatof | OCLC# 30932840 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.lcc | LD5655.V856 1994.B663 | en |
| dc.subject.lcsh | Periodic functions | en |
| dc.subject.lcsh | Spline theory | en |
| dc.title | A duality approach to spline approximation | en |
| dc.type | Dissertation | en |
| dc.type.dcmitype | Text | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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