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S. Karlin, W. J. Studden (1966)
Tchebycheff Systems: with Applications in Analysis and Statistics
E. Passow (1977)
Polynomials with Positive Coefficients: Uniqueness of Best ApproximationJournal of Approximation Theory, 21
Ying-guang Shi (1982)
Uniform Approximation by Generalized Polynomials having Bounded CoefficientsActa Mathematicae Applicatae Sinica, 5
Let the set of generalized polynomials haviug bounded coefficients be $$K = \left\{ {p = \sum\limits_{j = 1}^n {a_j g_j :a_j \in [a_j ,\beta _j ]} ,j = 1,2,...,n} \right\},$$ whereg 1,g 2, ...,g n are linearly independent continuous functions defined on the interval [a, b],α j ,β j are extended real numbers satisfyingα j <+∞,β j >−∞ andα j ⩽β j . Assume thatf is a continuous function defined on a compact setX ⊂ [a, b]. In the paper, we first give the sufficient conditions for the polynomial of best uniform approximation tof fromK being unique and strongly unique. Furthermore, we give two forms of necessary and sufficient conditions for the best approximation to be strongly unique.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 13, 2005
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