Maximal order for quadratures using n evaluations.
Mean-Square Discrepancies of the Hammersley and Zaremba Sequences for Arbitrary Radix.
Mehrdimensionale Hermite-Interpolation und numerische Integration.
Metric theorems on the estimation of integrals by sums
Moment computation in shift invariant spaces.
Moment preserving spline approximation finite intervals and Chakalov-Popoviciu quadratures.
Monosplines and inequalities for the remainder term of quadrature formulas.
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...