Moment-preserving spline approximation on finite intervals
The authors discuss the problem of approximating a function f on the interval [0,1] by a spline function of degree m, with n (variable) knots, matching as many of the initial moments of f as possible. Additional constraints on the derivates of the approximation at one endpoint of [0,1] may also be imposed. They show that, if the approximations exist, they can be represented in terms of generalized Gauss-Lobatto and Gauss- Radau quadrature rules relative to appropriate moment functionals or measures (depending on f). Pointwise convergence as \(n\to \infty\), for fixed \(m>0\), is shown for functions f that are completely monotonic on [0,1], among others. Numerical examples conclude the paper.
scientific article; zbMATH DE number 4050195