Szasz-Mirakyan Quasi-interpolants

Diallo, Aboubacar

doi:10.1016/b978-0-12-438660-0.50025-x

Cited by 7 publications

(6 citation statements)

References 2 publications

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“…This has been proved ( [6,7,8,9,21]) for Bernstein and Szász-Mirakyan operators and their associated Durrmeyer versions, and also for Kantorovich operators.…”

Section: Introductionmentioning

confidence: 94%

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Weierstrass quasi-interpolants

Sablonnière

2014

Journal of Approximation Theory

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“…This has been proved ( [6,7,8,9,21]) for Bernstein and Szász-Mirakyan operators and their associated Durrmeyer versions, and also for Kantorovich operators.…”

Section: Introductionmentioning

confidence: 94%

“…For example by M.W. Müller [16] to Gamma operators, by A.T. Diallo [6,8,9] and others to Szász-Mirakyan operators. In this paper, the expression of Weierstrass operators as differential operators on polynomials is used for the construction of associated quasi-interpolants.…”

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confidence: 99%

Weierstrass quasi-interpolants

Sablonnière

2014

Journal of Approximation Theory

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“…For example by P. Mache and M.W. Müller [8] to Baskakov operators, by A.T. Diallo [3,5,6] and the author [11] to Szász-Mirakyan operators, and more recently [14] to Weierstrass operators. This general method also works for multivariate extensions of these operators (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Approximation by Baskakov quasi-interpolants

Sablonnière

2013

Preprint

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Baskakov operators and their inverses can be expressed as linear differential operators on polynomials. Recurrence relations are given for the computation of these coefficients. They allow the construction of the associated Baskakov quasi-interpolants (abbr. QIs). Then asymptotic results are provided for the determination of the convergence orders of these new quasi-interpolants. Finally some results on the computation of these QIs and the numerical approximation of functions defined on the positive real half-line are illustrated by some numerical examples.

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“…[70] [86] for some results of this type). From this property are deduced some convergence results (see [30][67]).…”

Section: Left and Right Bqismentioning

confidence: 99%

Recent Progress on Univariate and Multivariate Polynomial and Spline Quasi-interpolants

Sablonnière

2005

Trends and Applications in Constructive Approximation

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Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to solve), uniform boundedness independently of the degree (polynomials) or of the partition (splines), good approximation order. We shall emphasize new results on various types of univariate and multivariate polynomial or spline QIs, depending on the nature of coefficient functionals, which can be differential, discrete or integral. We shall also present some applications of QIs to numerical methods.

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Szasz-Mirakyan Quasi-interpolants

Cited by 7 publications

References 2 publications

Weierstrass quasi-interpolants

Weierstrass quasi-interpolants

Approximation by Baskakov quasi-interpolants

Recent Progress on Univariate and Multivariate Polynomial and Spline Quasi-interpolants

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