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.
Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration
Modifications of Newton-Cotes formulas for computation of repeated integrals and derivatives
Standard algorithms for numerical integration are defined for simple integrals. Formulas for computation of repeated integrals and derivatives for equidistant domain partition based on modified Newton-Cotes formulas are derived. We compare usage of the new formulas with the classical quadrature formulas and discuss possible application of the results to solving higher order differential equations.
Modified Gauss-Legendre, Lobatto and Radau cubature formulas for the numerical evaluation of 2-D singular integrals.
Modified optimal quadrature extensions.
Moment preserving spline approximation finite intervals and Chakalov-Popoviciu quadratures.
Moment-Preserving Spline Approximation on Finite Intervals.
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...