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IOE 899: Seminar in Industrial and Operations Engineering
Wed Oct 7, 2009, 4:00-5:00pm, 1680 IOE

Shu-Cherng Fang, North Carolina State University
"Recent Progress on Shape-preserving Splines"

Abstract
Splines have been conveniently and widely used for drawing curves in two or three-dimensional spaces. Spline functions possess many nice structural properties and exhibit excellent approximation power. For real-world applications, one fundamental requirement for splines is that they should be “shape preserving” which, in general, means no “nonphysical” or “extraneous” oscillations. Observation over past three decades indicates traditional polynomial splines have inadequate shape-preserving capability, in particular, for data with arbitrary changes in magnitude and in node spacing. Experiments have shown that cubic L1 splines preserve shape well even for irregular data. We report our progress made in the past several years on developing the theory of shape-preserving cubic L1 splines for real-life applications in urban terrain description, CAD, and term structure analysis of bond market.
 
Bio
Shu-Cherng Fang is appointed the Walter Clark Chair and Alumni Distinguished Graduate Professor in the Department of Industrial Engineering and Gradute Program in Operations Research at NC State University. His research interests include variational inequalities, large-scale linear and nonlinear programming, entropy optimization, neural computing and fuzzy systems theory, with applications to building intelligent human-machine decision support systems for manufacturing, supply chain management, logistics, telecommunications and informatics. Professor Fang received his Bachelor's degree from The National Tsing Hua University in Taiwan (1974), Master's degree from The Johns Hopkins University (1977), and PhD degree from Northwestern University (1979). Before he joined NC State in 1988, Dr. Fang had been with the University of Maryland, AT&T Engineering Research Center, AT&T Bell Laboratories, and AT&T Corporate Headquarters. Professor Fang has published a few journal articles and book chapters. He is the author of Linear Optimization and Extensions: Theory and Algorithms (Prentice Hall 1993) and Mathematical Programming and Entropy Optimization (Kluwer Academic Publishers 1997). He is also the Founding Editor-in-Chief of Fuzzy Optimization and Decision Making (Springer 2000). Professor Fang is a Fellow of the Institute of Industrial Engineers.

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