1. What are the contributions mentioned in the paper "Algorithms for positive polynomial approximation" ?
The authors propose several algorithms for positive polynomial approximation.. Their method is based on the special representations of non negative polynomials provided by the Lukács Theorem, and a key point is the use of Chebyshev polynomials for the initial step of the iterations.
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2. What is the main case of the two main cases?
The two main cases are • either qλ ∈ P+4 , then pm4 ∈ P+4 is very close to qλ • or qλ 6∈ P+4 , then pm4 ∈ P+4 can be used as a non negative polynomial surrogate tothe objective function qλ.
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3. What is the way to estimate a polynomial?
The approximation by positive interpolation polynomials is optimal in terms of polynomial degree, and so is optimal in terms of accuracy.
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4. What is the first step in the iteration loop?
Pn with n = 2p + 1; in a second stage the authors use the iteration loop (3.8) with m = p steps; it yields a local polynomial p̃n ∈ P+n which is a high order approximation of pn.
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