The main objective of this research is the study of computational and constructive aspects of orthogonal polynomials. Special attention is to be given to the development and analysis of constructive methods for generating orthogonal polynomials of Sobolev type, i.e., polynomials that are orthogonal with respect to an inner product involving derivatives. These have originally been introduced to approximate functions and their derivative simultaneously, and have since received a considerable amount of attention but largely from approximation-theoretic and algebraic points of view and with little regard to computational aspects. Other topics to be considered involve the question of computing polynomials orthogonal relative to a Hermite weight on a finite interval and the analysis of the remainder terms of special quadrature rules. Orthogonal polynomials are basic tools of approximation. They provide orthogonal expansions and least square approximations to functions and contribute to a variety of quadrature processes. In addition they are used extensively in the numerical solution of ordinary differential equations and in the application of iterative methods for solving systems of linear algebraic equations.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
9305430
Program Officer
Joe W. Jenkins
Project Start
Project End
Budget Start
1993-07-01
Budget End
1997-06-30
Support Year
Fiscal Year
1993
Total Cost
$135,000
Indirect Cost
Name
Purdue Research Foundation
Department
Type
DUNS #
City
West Lafayette
State
IN
Country
United States
Zip Code
47907