Generally, classical polynomial splines tend to exhibit unwanted
undulations. In this work, we discuss a technique, based on control
principles, for eliminating these undulations and increasing the
smoothness properties of the spline interpolants. We give a
generalization of the classical polynomial splines and show that
this generalization is, in fact, a family of splines that covers
the broad spectrum of polynomial, trigonometric and exponential
splines. A particular element in this family is determined by the
appropriate control data. It is shown that this technique is easy
to implement. Several numerical and curve-fitting examples are
given to illustrate the advantages of this technique over the
classical approach. Finally, we discuss the convergence properties
of the interpolant.
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