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Simultaneous Polynomial Approximation

SIAM Journal on Mathematical Analysis, 1993
The authors prove the approximation theorem on simultaneous approximation of \(f\in C^ s[- 1,1]\) and its derivatives of order \(j\), \(0\leq j\leq s\), by polynomials of degree \(n\) and their derivatives which has filled the gap between Timan-Trigub's type theorem and the classical norm estimate of the Jackson type.
Ditzian, Z.   +2 more
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Weighted Polynomial Approximations

2001
In this chapter, we establish the existence of weighted polynomial approximations that are a prerequisite to the estimates and asymptotics in subsequent chapters. We search for polynomials P n of degree n such that P n W approximates 1 in some sense on [a −n, a n ].
Eli Levin, Doron S. Lubinsky
openaire   +1 more source

m-approximate Taylor polynomial

manuscripta mathematica, 2019
In \(\mathbb{R}^n\) a notion of \(m\)-density for \(m\in [n, \infty)\) is a generalization of density. Analogous as approximate continuity (differentiability) one can define \(m\)-approximate continuity (differentiability) at a point. It is proved that if \(1\leq p< \infty\) and \(f\colon \mathbb{R}^n \to \mathbb{R}\) is \(L^p\) differentiable at \(x ...
openaire   +3 more sources

Approximation Numbers for Polynomials

2019
Approximation numbers of linear operators are a very useful tool in order to understand the structure and the numerical behaviour of the operators. In this paper, this concept is extended to polynomials on Banach spaces and the approximation numbers of diagonal polynomials are estimated.
Junek, Heinz   +2 more
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Approximate Polynomial GCD by Approximate Syzygies

Mathematics in Computer Science, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Probability measures, appel polynomials and polynomial approximation

Applied Mathematics and Computation, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Martin, Clyde, Shubov, Victor
openaire   +2 more sources

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