Nonlinear Regression with Emphasis on Spline Methods.
Abstract
Spline functions with variable knots have been very useful in nonlinear regression and approximation. For example, shape-preserved curve fitting can be adjusted to give optimal degree of approximation, and uniqueness, computational methods etc. have also been studied. To further investigate the local behavior of best approximants, the idea of best local approximation was introduced. This relates the original problem to three important areas of research, namely: Pade approximants, recursive digital filter realization, and certain minimax approximation problems. In order to give meaningful investigation into these areas, techniques from Functional Analysis and Operator Theory have been used, and related but quite general results on Approximation Theory have also been found. In studying multi-variable regression, it was noted that tensor-product splines have very limited applications. Hence, basic theory and results concerning dimensions, bases, B-splines, interpolation, etc. on bivariate, and sometimes multivariate, non-tensor product splines have been obtained. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 02, 1984
- Accession Number
- ADA146192
Entities
People
- Charles K. Chui
- J. D. Ward
- P. W. Smith
Organizations
- Texas A&M University