Accession Number : AD0707620

Title :   SPLINE FUNCTIONS AND APPLICATIONS.

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Greville,T. N. E.

Report Date : 1969

Pagination or Media Count : 107

Abstract : The document begins with a definition of a spline function, some general remarks about the nature and uses of such functions, an illustrative example, and a simple algebraic representation for any spline function. The important subclass of natural splines is defined in chapter 2 and the theorem of unique interpolation by natural splines and the well known minimal property of the smoothest interpolating natural spline is proven. Chapter 3 is concerned with the approximation of linear functionals. It includes Peano's theorem on remainders, A. Sard's theory of best approximation of linear functionals, and I.J. Schoenberg's discovery that finding the best approximation to a given functional in Sard's sense is equivalent to applying the functional to the corresponding natural spline interpolating function. Chapter 4 develops the properties of divided differences and of the B-splines, a special type of spline functions with limited support that constitute a basis for the class of spline functions and are important for computational purposes. Chapter 5 concerns a numerical algorithm for obtaining the natural spline interpolating function and also considers the smoothing natural splines resulting from Schoenberg's adaptation of E. T. Whittaker's smoothing method. (Author)

Descriptors :   (*FUNCTIONS(MATHEMATICS), *APPROXIMATION(MATHEMATICS)), DIFFERENTIAL EQUATIONS, INTERPOLATION, NUMERICAL ANALYSIS, NUMERICAL INTEGRATION, POLYNOMIALS, THEOREMS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE