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- Abdelkrim Ezzirani, Allal Guessab
- Math. Comput.
- 1999

After studying Gaussian type quadrature formulae with mixed boundary conditions, we suggest a fast algorithm for computing their nodes and weights. It is shown that the latter are computed in the… (More)

- Allal Guessab
- 1994

Abstract In this paper we give a new characterization of the classical orthogonal polynomials (Hermite, generalized Laguerre, Jacobi) by extremal properties in some weighted polynomial inequalities… (More)

- Allal Guessab
- 1995

- Allal Guessab, Gerhard Schmeisser
- Math. Comput.
- 2003

jjAn interesting property of the midpoint rule and the trapezoidal rule, which is expressed by the so-called Hermite-Hadamard inequalities, is that they provide one-sided approximations to the… (More)

- Allal Guessab, Gerhard Schmeisser
- Journal of Approximation Theory
- 2002

We consider a family of two-point quadrature formulae and establish sharp estimates for the remainders under various regularity conditions. Improved forms of certain integral inequalities due to… (More)

- Allal Guessab, Otheman Nouisser, Josip Pečarić
- 2012

In this paper, we present a more general and extended form in a multivariate setting of an inequality of Brenner and Alzer.

We study an approximation of a multivariate function f by an operator of the form Σi=1N˜r|f, xi|(x)φi(x), where φ1,...,φN are certain basis functions and ˜r|f, xi|(x) are modified Taylor polynomials… (More)

- Allal Guessab, Gerhard Schmeisser
- Adv. Comput. Math.
- 2008

Let Ω ⊂ ℝd be a compact convex set of positive measure. In a recent paper, we established a definiteness theory for cubature formulae of order two on Ω. Here we study extremal properties of those… (More)

AbstractLet Ω be a compact convex domain in $${\mathbb{R}}^{d}$$ and let L be a bounded linear operator that maps a subspace of C(Ω) into C(Ω). Suppose that L reproduces polynomials up to degree m.… (More)

Let Ω ⊂ ℝd be a compact convex set of positive measure. A cubature formula will be called positive definite (or a pd-formula, for short) if it approximates the integral ∫Ω f(x) dx of every convex… (More)