Note on Error Bounds for Numerical Integration

A Note on Error Bounds for Convex and Nonconvex Programs

Given a single feasible solution xF and a single infeasible solution xI of a mathematical program, we provide an upper bound to the optimal dual value. We assume that xF satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to Mangasarian [11] on the distance of a poi...

Error bounds for kernel-based numerical differentiation

The literature on meshless methods observed that kernel-based numerical differentiation formulae are robust and provide high accuracy at low cost. This paper analyzes the error of such formulas, using the new technique of growth functions. It allows to bypass certain technical assumptions that were needed to prove the standard error bounds on interpolants and their derivatives. Since differenti...

A Note on Haselgrove's Method for Numerical Integration

An alternative set of weights is proposed for Niederreiter's generalization of Haselgrove's method for numerical integration. 1. In 1961, C. B. Haselgrove [1] introduced effective J-dimensional cubature formulas for a certain class of integrand functions over Gd i=[0,l]d) which were generalized by H. Niederreiter [2], [3]. But the generalized cubatures are not necessarily easy to handle. Here w...

An Error Analysis for Numerical Multiple Integration

A Note on Error Bounds For1 Convex and Nonconvex Programs

Given a single feasible solution xF and a single infeasible solution xI of a mathematical program, we provide an upper bound to the optimal dual value. We assume that xF satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to Mangasarian [Man97] on the distance of a ...