Document Type

Dissertation

Degree

Doctor of Philosophy

Major

Mathematics

Date of Defense

9-30-2009

Graduate Advisor

Wenjie He, PhD.

Committee

George Taylor

Jiang, Qingtang

Cai, Haiyan

Abstract

This dissertation is concerned with the problem of constructing biorthogonal wavelets based on non-uniform rational cubic B-Splines on intervals. We call non-uniform rational B-Splines ``NURBs", and such biorthogonal wavelets ``NURBlets". Constructing NURBlets is useful in designing and representing an arbitrary shape of an object in the industry, especially when exactness of the shape is critical such as the shape of an aircraft. As we know presently most popular wavelet models in the industry are approximated at boundaries. In this dissertation a new model is presented that is well suited for generating arbitrary shapes in the industry with mathematical exactness throughout intervals; it fulfills interpolation at boundaries as well.

Included in

Mathematics Commons

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