Accession Number : ADA118974

Title :   Polynomial Approximation: The Weierstrass Approximation Theorem.

Descriptive Note : Master's thesis,

Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH

Personal Author(s) : Nichols,Shirley Jo

PDF Url : ADA118974

Report Date : Aug 1982

Pagination or Media Count : 31

Abstract : In this paper we will look at three proofs of the Weierstrass Approximation Theorem. The first proof is in much the same form in which Weierstrass originally proved his theorem. The next is due to Lebesgue. It is by far the easiest proof to follow, with only a minimum knowledge of analysis required. The last arises from probability and uses the Bernstein polynomials. Secondly we look at a generalization of this theorem, called the Stone-Weierstrass Theorem. This generalization was inspired by modern developments in mathematics. The theorem deals with functions on a general compact space rather than on a closed interval.

Descriptors :   *Polynomials, *Approximation(Mathematics), Continuity, Functions(Mathematics), Probability, Intervals, Theorems, Theses

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE