TY  - BOOK
AU  - Subrahmanya, M.R.
TI  - Topics on Simultaneous best approximation
PY  - 1974///
KW  - Mathematics
KW  - Algebraic Polynomials
KW  - General Chebyshev's System
N1  - 1974
N2  - 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
UR  - http://www.imsc.res.in/xmlui/handle/123456789/41
ER  -