Topics on Simultaneous best approximation

DSpace/Manakin Repository

Topics on Simultaneous best approximation

Show full item record

Title: Topics on Simultaneous best approximation
Author: Subrahmanya, M.R.
Advisor: Unni, K. R.
Degree: Ph.D
Main Subjects: Mathematics
Institution: Others
Year: 1974
Pages: iv; 92p.
Abstract: In 1968 Rivlin posed a problem on Algebraic Polynomial; "Characterise those n-tuples {P1, P2, ... P(n-1)}of algebraic polynomials such that the degree of Pj is j for j = 0,1,2,..., n-1., for which there exists a real valued continuous function f defined on a closed and finite interval, [a,b] so that the polynomial of best approximation of degree j for f in the sense of Chebyshev, is Pj, j = 0,1,2, ... , n-1". He suggested the necessary condition that, " Suppose there exists a continuous real valued function f defined on [a,b], such that Pj is the polynomial of best approximation, to f of degree j. Then for each pair of indices, i, k, 0 < (or) = i < K < (or) = (n-1). The polynomial Pi - Pk is either identically zero or changes sign atleast (i+1) distinct points in [a,b]. This thesis study the problem for algebraic polynomials and also for General Chebyshev system, and obtain necessary and sufficient conditions. Further various related problems are also discussed.
URI: http://hdl.handle.net/123456789/41

Files in this item

Files Size Format View
UNMTH18.pdf 4.691Mb PDF View/Open

This item appears in the following Collection(s)

Show full item record

Search DSpace


Advanced Search

Browse

My Account