Theoretical Explanation of Bernstein Polynomials’ Efficiency: They Are Optimal Combination of Optimal Endpoint-Related Functions∗
نویسندگان
چکیده
In many applications of interval computations, it turned out to be beneficial to represent polynomials on a given interval [x, x] as linear combinations of Bernstein polynomials (x − x) · (x − x)n−k. In this paper, we provide a theoretical explanation for this empirical success: namely, we show that under reasonable optimality criteria, Bernstein polynomials can be uniquely determined from the requirement that they are optimal combinations of optimal polynomials corresponding to the interval’s endpoints.
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