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Moment-preserving spline approximation on finite intervals. (English) Zbl 0644.41005
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.
Reviewer: A.Bleyer

MSC:
41A15 Spline approximation
65D32 Numerical quadrature and cubature formulas
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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References:
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