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Degree of Simultaneous Coconvex Polynomial Approximation

Results in Mathematics, 1998
Let \(f\in C^1[-1,1]\) change its convexity \(s\)-times at the points \(y_j\in (-1,1)\) \((j-1, \dots,s)\). Then \(f\) is approximated by polynomials \(p_n\), which are coconvex with \(f\), i.e., \(p_n\) changes its convexity exactly at the same points \(y_j\) \((j=1, \dots,s)\).
Kopotun, K., Leviatan, D.
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THE DEGREE OF RATIONAL APPROXIMATION OF FUNCTIONS AND THEIR DIFFERENTIABILITY

Mathematics of the USSR-Izvestiya, 1981
Translation from Izv. Akad. Nauk SSSR, Ser. Mat. 44, 1410-1416 (Russian) (1980; Zbl 0479.41013).
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Interpretations of Lower Approximations in Inclusion Degrees

2016
The nature of uncertainty inference is to give evaluations on inclusion relationships by means of various measures. In this paper we introduce the concept of inclusion degrees into rough set theory. It is shown that the lower approximations of the rough set theory in both the crisp and the fuzzy environments can be represented as inclusion degrees.
Wei-Zhi Wu 0001, Chao-Jun Chen, Xia Wang
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Approximation of Higher Degree

2016
The m wedge basis functions for a polycon of order m and products of these functions may be used to fit discrete data on polycon sides while maintaining continuity across polycon boundaries. The side between vertices i and i + 1 in Fig. 6.1 is a conic boundary component with side node p.
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A Survey of Degree of Approximation of Continuous Functions

SIAM Review, 1981
The purpose of this paper is to give a survey of results in the study of direct theorems in degree (or order) of “best approximation” $E_n (f)$, of a function $f(x)$, by trigonometric polynomials. We will normally require the function $f(x)$ to be $2\pi $-periodic and integrable in the Lebesgue sense. Further differentiability conditions may be imposed
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Degree of Monotone Approximation

1974
We are interested in approximating monotone functions by monotone polynomials. Denote by ∏n, the space of algebraic polynomials of degree ≤ n, and by ∏*n, the set of those polynomials in ∏n which are monotone non-decreasing on the interval [−1,1].
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Degree of approximation of analytic functions by “near the best” polynomial approximants

Constructive Approximation, 1993
Let \(K\) be a compact subset of the complex plane \(\mathbb{C}\) such that \(\mathbb{C} - K\) is connected. Given a function \(f \in A (K)\), let \(E_n (f) : = \inf \{|f - p_n |_K; \deg p_n \leq n\}\) be the error of the best uniform approximation to \(f\) by polynomials of degree at most \(n\). Following \textit{E. B. Saff} and \textit{V.
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