http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Computational aspects of spline-wavelets
This dissertation deals with two topics on spline-wavelets
with minimal support. Part one. Fast block-realtime
algorithms for cardinal spline interpolation and cardinal
spline-wavelet decomposition suitable for large data sets are
presented. In order to find an interpolating cardinal spline
on the real line, the given sequence of input values is
partitioned into blocks of finite length. The interpolation
algorithm is based on the factorization of the Euler-
Frobenius polynomial, and on forward/backward substitution
applied to one block at a time. The spline-wavelet
decomposition is viewed as a cardinal spline interpolation
problem of even order, and the interpolation algorithm is
applied. An error analysis demonstrates the stability of the
algorithm. The decomposition algorithm has only 2 to 3 times
the numerical complexity of the reconstruction, and hence is
very efficient. Numerical examples illustrate the
algorithms. Part two. Minimally supported spline-wavelets
with multiple non-uniform knots on a bounded interval are
considered. General knot refinements of arbitrarily many new
knots between two old knots are allowed. A spline-wavelet of
order in with minimal support is constructed as the 7n-th
derivative of a locally supported spline of order 2m
satisfying certain Hermite-interpolation conditions, The
interpolation problem leads to a system of linear equations
with a positive definite, skew-banded coefficient matrix to
which LU-factorization can be applied without destroying its
zero-entry structure. This provides an efficient method for
the construction of a minimally supported spline-wavelet
basis. A decomposition algorithm is developed based on
Hermite-interpolation. Knot insertion is used for the
reconstruction. The algorithms are tested and numerical
Issued also on microfiche from University Microfilms Inc.
Includes bibliographical references: pages 114-116.