OPTIMAL INTERPOLATING AND OPTIMAL SMOOTHING SPLINE

Jitka Machalová

   In this paper we will consider spline functions in the interpolation, least squares problem and smoothing problem. We will use free parameters to minimize some functionals with geometrical or physical meaning ( urvature, energy) and we will describe necessary and sufficient conditions under which the required spline exists and is unique. To get this spline we shall use the B-spline basis and generalized inverses of some matrix.

Keywords: spline, B-spline basis, interpolation, smoothing, generalized inverse of a matrix

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