Abstract
The approximation properties of polynomial splines in a convex set are studied. For splines of first degree, error estimates are obtained for approximating a function in a uniform metric, and its first derivative in the norm of space L 2[ a, b], and in the case of splines of the third degree, a function and its first derivative in a uniform norm, and its second derivative, in the norm of L 2[ a, b]. It follows from the form of the estimates that the operation of numerical differentiation by means of splines in a convex set is well-posed in the sense of stability under peturbations of the input data.
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