Abstract
Forward interpolation, as discussed here, refers to the problem of interpolating data points revealed, one at a time, in a sequential manner. As such, forward spline interpolation is an inherently unstable process. In this paper we study forward interpolation using a class of “generalized splines”: piecewise polynomials of odd degree $2m-1$, continuous to order $m-1$, where $m\ge 2$ is an integer. We show that the problem can be interpreted as a state estimation problem for a discrete linear system and show how successful, stable procedures can be obtained by applying optimal state estimation techniques of “LQG” type long familiar in the theory of such systems. A number of examples are presented.
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