Bonawitz, Elizabeth Ann2014-03-142014-03-141994-04-21etd-03022006-093404http://hdl.handle.net/10919/37448This 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.viii, 112 leavesBTDapplication/pdfenIn CopyrightLD5655.V856 1994.B663Periodic functionsSpline theoryA duality approach to spline approximationDissertationhttp://scholar.lib.vt.edu/theses/available/etd-03022006-093404/