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Counterexamples in best approximation [PDF]
Proceedings of the American Mathematical Society, 1976 Several counterexamples for approximation to continuous functions by polynomials are given. One example shows that the points of maximum deviation of a continuous real valued function on an interval from its polynomial of degree n n of best uniform approximation can lie on any monotone sequence contained in that interval for ...
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Approximating gradients with continuous piecewise polynomial functions [PDF]
, 2014 Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh.
Veeser, Andreas
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Robust Localization of the Best Error with Finite Elements in the Reaction-Diffusion Norm [PDF]
, 2014 We consider the approximation in the reaction-diffusion norm with continuous finite elements and prove that the best error is equivalent to a sum of the local best errors on pairs of elements.
Tantardini, Francesca +2 more
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Separable approximations of density matrices of composite quantum systems [PDF]
, 2000 We investigate optimal separable approximations (decompositions) of states rho of bipartite quantum systems A and B of arbitrary dimensions MxN following the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261 (1998)].
Bennett C H +23 more
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Best approximation in Orlicz spaces
International Journal of Mathematics and Mathematical Sciences, 1991 Let X be a real Banach space and (Ω,μ) be a finite measure space and ϕ be a strictly icreasing convex continuous function on [0,∞) with ϕ(0)=0. The space Lϕ(μ,X) is the set of all measurable functions f with values in X such that ∫Ωϕ(‖c−1f(t)‖)dμ(t)0 ...
H. Al-Minawi, S. Ayesh
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Approximation algorithms for node-weighted prize-collecting Steiner tree problems on planar graphs [PDF]
, 2016 We study the prize-collecting version of the Node-weighted Steiner Tree problem (NWPCST) restricted to planar graphs. We give a new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for planar NWPCST.
Byrka, Jarosław +2 more
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Best Approximation from the Kuhn-Tucker Set of Composite Monotone Inclusions [PDF]
, 2014 Kuhn-Tucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions.
Abdullah M. Alotaibi +2 more
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Some best approximation formulas and inequalities for the Wallis ratio [PDF]
Applied Mathematics and Computation, 2013 In the paper, the authors establish some best approximation formulas and inequalities for the Wallis ratio. These formulas and inequalities improve an approximation formula and a double inequality for the Wallis ratio presented in 2013 by three ...
Feng Qi (祁锋), C. Mortici
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Continuity of best approximants [PDF]
Proceedings of the American Mathematical Society, 1981 Let C n {C_n} , n ∈ N n \in {\mathbf {N}} , be Φ \Phi -closed lattices in an Orlicz-space L Φ ( Ω , A
Landers, D., Rogge, L.
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Best Approximation Results for Fuzzy-Number-Valued Continuous Functions
Axioms, 2023 In this paper, we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions.
Juan J. Font, Sergio Macario
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