Results 291 to 300 of about 194,210 (329)

Simultaneous Approximation of Polynomials

2016
Let \(\mathcal{P}_d\) denote the family of all polynomials of degree at most d in one variable x, with real coefficients. A sequence of positive numbers \(x_1\le x_2\le \ldots \) is called \(\mathcal{P}_d\)-controlling if there exist \(y_1, y_2,\ldots \in \mathbb {R}\) such that for every polynomial \(p\in \mathcal{P}_d\) there exists an index i with \(
Andrei Kupavskii, János Pach
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Approximation by Chlodowsky–Taylor polynomials

Applied Mathematics and Computation, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sevilay Kirci Serenbay, Ertan Ibikli
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Complexity and Approximability of the Cover Polynomial

computational complexity, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Markus Bläser, Holger Dell, Mahmoud Fouz   +2 more
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Monotone Approximation by Polynomials

SIAM Journal on Mathematical Analysis, 1977
We prove Jackson type estimates for the approximation of monotone functions by monotone polynomials. The results are given in terms of the modulus of continuity of $f^{(k)} $ , for any $k \geqq 0$. The estimates are of the same order as for the unconstrained approximation by polynomials.
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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
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Approximation by Bernstein Polynomials

American Journal of Mathematics, 1994
Let \[ B_ n(f; x)= \sum^ n_{k=0} f\left({k\over n}\right)\left(\begin{smallmatrix} n\\ k\end{smallmatrix}\right) x^ k(1-x)^{n- k} \] and \(w_ \varphi(f; \delta)= \sup_{0\leq t\leq \delta} \sup_ x| f(x- t\varphi(x))- 2f(x)+ f(x+ t\varphi(x)))|\), where \(f\in C[0,1]\), \(\varphi(x)= \sqrt{x(1-x)}\) and the second supremum is taken for those values of ...
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Approximation by $\delta $-Polynomials

SIAM Journal on Numerical Analysis, 1973
The approximation to complex-valued functions, continuous on a closed Jordan curve by polynomials of degree n, whose uniform norm on that curve is greater than or equal to some prescribed constant, is investigated. The limits for the resultant sequence of the best such deviations are found for a large class of functions.
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Approximation of analytic functions by polynomials ?close? to polynomials of best approximation

Ukrainian Mathematical Journal, 1992
See the review in Zbl 0758.30034.
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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 ...
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Approximation with Polynomials

2004
In many applications of mathematics, we face functions which are far more complicated than the standard functions from classical analysis. Some of these functions can not be expressed in closed form via the standard functions, and some are only known implicitly or via their graph.
Ole Christensen, Khadija L. Christensen
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