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Browsing by Author "Bonawitz, Elizabeth Ann"

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    A duality approach to spline approximation
    Bonawitz, Elizabeth Ann (Virginia Tech, 1994-04-21)
    This dissertation discusses a new approach to spline approximation. A periodic spline approximation 𝑓M,m,N(x) = Σk=1NαkΦM,k(x) to a periodic function 𝑓(x) is determined by requiring < Φm,j, 𝑓 - 𝑓M,m,N > = 0 for j = 1,...,N, where the ΦL,k'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.