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Minimax polynomial approximation [PDF]
Mathematics of Computation, 1966 Some new methods for obtaining the minimax polynomial approximation of degree n n to a continuous function are introduced ...
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On a polynomial approximation problem
Journal of Approximation Theory, 2010 AbstractLet F be a closed subset of the unit circle T and let f∈C(F). We investigate the problem of uniform approximation of f on F by polynomials Pn which are uniformly bounded on the unit disk Δ. In a particular case when F is a closed arc of T, the problem was solved by L. Zalcman in 1982, who has also pointed out the possibility of considering more
Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA ( host institution ) +1 more
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Szász-Durrmeyer operators involving Boas-Buck polynomials of blending type
Journal of Inequalities and Applications, 2017 The present paper introduces the Szász-Durrmeyer type operators based on Boas-Buck type polynomials which include Brenke type polynomials, Sheffer polynomials and Appell polynomials considered by Sucu et al. (Abstr. Appl. Anal. 2012:680340, 2012).
Manjari Sidharth +2 more
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Open Mathematics, 2021 Fourier approximation plays a key role in qualitative theory of deterministic and random differential equations. In this paper, we will develop a new approximation tool.
Zhang Zhihua
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Weighted Approximation for Jackson-Matsuoka Polynomials on the Sphere
Abstract and Applied Analysis, 2012 We consider the best approximation by Jackson-Matsuoka polynomials in the weighted Lp space on the unit sphere of Rd. Using the relation between K-functionals and modulus of smoothness on the sphere, we obtain the direct and inverse estimate of ...
Guo Feng
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Approximation by homogeneous polynomials [PDF]
Journal of Approximation Theory, 2013 Uniform approximations by even degree homogeneous polynomials are considered. For a centrally symmetric convex set with nonempty interior, all even continuous functions on its boundary (in two space dimensions; the problem is open for higher dimensions) can be uniformly approximated by them. This is a new, more elementary proof of this fact.
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Approximating a Norm by a Polynomial [PDF]
, 2003 We prove that for any norm |*| in the d-dimensional real vector space V and for any odd n>0 there is a non-negative polynomial p(x), x in V of degree 2n such that p^{1/2n}(x) < |x| < c(n,d) p^{1/2n}(x), where c(n,d)={n+d-1 choose n}^{1/2n}. Corollaries and polynomial approximations of the Minkowski functional of a convex body are discussed.
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On the Approximation of the Jacobi Polynomials
Rocky Mountain Journal of Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Elias, Uri, Gingold, Harry
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Algorithms For Positive Polynomial Approximation [PDF]
SIAM Journal on Numerical Analysis, 2019 Summary: We propose several algorithms for positive polynomial approximation. The main tool is a novel iterative method to compute nonnegative interpolation polynomials at any order, which is shown to converge under conditions that make it suitable for the numerical approximation of positive functions. Our method is based on the special representations
Charles, Frédérique +2 more
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Approximating Polynomials for Functions of Weighted Smirnov-Orlicz Spaces
Journal of Function Spaces and Applications, 2012 Let 𝐺0 and 𝐺∞ be, respectively, bounded and unbounded components of a plane curve Γ satisfying Dini's smoothness condition. In addition to partial sum of Faber series of 𝑓 belonging to weighted Smirnov-Orlicz space 𝐸𝑀,𝜔 (𝐺0), we prove that interpolating ...
Ramazan Akgün
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