# Topics on Simultaneous best approximation

 dc.contributor.author Subrahmanya, M.R. dc.date.accessioned 2009-08-05T05:38:13Z dc.date.available 2009-08-05T05:38:13Z dc.date.issued 2009-08-05T05:38:13Z dc.date.submitted 1974 dc.identifier.uri http://hdl.handle.net/123456789/41 dc.description.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. en_US dc.subject Algebraic Polynomials en_US dc.subject General Chebyshev's System en_US dc.title Topics on Simultaneous best approximation en_US dc.type.degree Ph.D en_US dc.type.institution Others en_US dc.description.advisor Unni, K. R. dc.description.pages iv; 92p. en_US dc.type.mainsub Mathematics en_US

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