Publication Date

2019

Document Type

Dissertation/Thesis

First Advisor

Wang, Ziteng

Second Advisor

Damodaran, Purushothaman

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Industrial and Systems Engineering

Abstract

Cubic $L^1$ spline fits, as a type of $L^1$ approximating splines, have shown superior performance in shape preservation of geometric data with great changes. To better construct a cubic $L^1$ spline fit, the number and the location of the spline knots should be optimized rather than predetermined. This research investigates knot optimization methods for univariate cubic $L^1$ spline fits. When the number of knots is given, we design an optimization-based method to determine the best location of the knots. When the number and the location are unknown, we propose a heuristic method to find proper knot number and location. Numerical experiments show that cubic $L^1$ spline fits with optimized knots can better approximate data and preserve shapes. The cubic $L^1$ spline fits with optimized knots show good potential when applied in change point detection.

Extent

75 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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