Markoff-type inequalities in weighted -norms.
Matrices Related to Interpolatory Quadratures.
Matrix computation and the theory of moments.
Maximal order for quadratures using n evaluations.
Mehrdimensionale Hermite-Interpolation und numerische Integration.
Modified Gauss-Legendre, Lobatto and Radau cubature formulas for the numerical evaluation of 2-D singular integrals.
Modified optimal quadrature extensions.
Modifizierte Restgliedabschätzungen für Quadraturformeln.
Moment preserving spline approximation finite intervals and Chakalov-Popoviciu quadratures.
Monotonicity of Quadrature Formulae of Gauss Type and Comparison Theorems for Monosplines.
Monotonicity results for a compound quadrature method for finite-part integrals.
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...