Monotonicity and Error Bounds in Schemes of Romberg Type for the Computation of f(n) (0) by Central Differences and Extrapolation.
Monotonicity of Quadrature Formulae of Gauss Type and Comparison Theorems for Monosplines.
Monotony in Interpolatory Quadratures.
Multiple Zeros and Applications to Optimal Linear Functionals.
Multiple-Precision Correctly rounded Newton-Cotes quadrature
Numerical integration is an important operation for scientific computations. Although the different quadrature methods have been well studied from a mathematical point of view, the analysis of the actual error when performing the quadrature on a computer is often neglected. This step is however required for certified arithmetics. We study the Newton-Cotes quadrature scheme in the context of multiple-precision arithmetic and give enough details on the algorithms and the error bounds to enable software...
New error inequalities for the Lagrange interpolating polynomial.
Note sur le calcul de la table d'activité
Numerical Evaluation of Integrals of Periodic Functions with Cauchy and Poisson Type Kernels.
Numerical integration for high order pyramidal finite elements
We examine the effect of numerical integration on the accuracy of high order conforming pyramidal finite element methods. Non-smooth shape functions are indispensable to the construction of pyramidal elements, and this means the conventional treatment of numerical integration, which requires that the finite element approximation space is piecewise polynomial, cannot be applied. We develop an analysis that allows the finite element approximation space to include non-smooth functions and show that,...
Numerical integration for high order pyramidal finite elements
We examine the effect of numerical integration on the accuracy of high order conforming pyramidal finite element methods. Non-smooth shape functions are indispensable to the construction of pyramidal elements, and this means the conventional treatment of numerical integration, which requires that the finite element approximation space is piecewise polynomial, cannot be applied. We develop an analysis that allows the finite element approximation space to include non-smooth functions and show that,...
Numerical integration in the Trefftz finite element method
Using the high order Trefftz finite element method for solving partial differential equation requires numerical integration of oscillating functions. This integration could be performed, instead of classic techniques, also by the Levin method with some modifications. This paper shortly describes both the Trefftz method and the Levin method with its modification.
Numerical integration with weights of convex functions of algebraic polynomials
Numerical Iteration of Functions of Very Many Variables.
Numerical stability in dynamic elastic-plastic problems
Numerische Quadratur bei Projektionsverfahren.
On a New Type of Quadrature Formulas.
On a Number-Theoretical Integration Method.
On a Number-Theoretical Integration Method. (Short Communications).
On Equally Weighted Quadratures.
On -discrepancy and mixed Monte Carlo and quasi-Monte Carlo sequences.