On constrained uniform approximation.

Bokhari, M.A.

Displaying similar documents to “On constrained uniform approximation.”

The best uniform quadratic approximation of circular arcs with high accuracy

Abedallah Rababah (2016)

Open Mathematics

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In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical...

Algorithms 77-78. Uniform approximation of empirical functions being either monotone or having a fixed number of extrema

E. Pankowski (1980)

Applicationes Mathematicae

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On restricted derivative approximation

Zi-Xiao Yang, Bu-Xi Li (1990)

Compositio Mathematica

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On a Problem of Best Uniform Approximation and a Polynomial Inequality of Visser

M. A. Qazi (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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In this paper, a generalization of a result on the uniform best approximation of α cos nx + β sin nx by trigonometric polynomials of degree less than n is considered and its relationship with a well-known polynomial inequality of C. Visser is indicated.

On Uniqueness of Best L1-Approximation of Disjoint Intervals.

András Kroó (1986)

Mathematische Zeitschrift

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Approximation relative to an ultra function

Tulsi Dass Narang (1986)

Archivum Mathematicum

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On the approximation by compositions of fixed multivariate functions with univariate functions

Vugar E. Ismailov (2007)

Studia Mathematica

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The approximation in the uniform norm of a continuous function f(x) = f(x₁,...,xₙ) by continuous sums g₁(h₁(x)) + g₂(h₂(x)), where the functions h₁ and h₂ are fixed, is considered. A Chebyshev type criterion for best approximation is established in terms of paths with respect to the functions h₁ and h₂.

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

Kyurkchiev, Nikolay, Markov, Svetoslav (2015)

Serdica Journal of Computing

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We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric....