New methods for constructing flattest and smoothest models

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Abstract
Standard techniques for constructing flattest and smoothest models require the specification of additional information about the model. This extra information consists of an independent value of the model (in the flattest model case) or values for the model and its first derivative (in the smoothest model solution), and is typically prescribed at an endpoint of the interval of model definition. This conventional procedure is generalized in two important ways: (i) the extra information is supplied at arbitrary points within the interval, and (ii) optimum values for these parameters are calculated directly from the observed data. The latter method yields the absolutely flattest (or smoothest) model satisfying the data, and is particularly useful if an independent value of the model (and/or its slope) is difficult to estimate accurately. Both techniques are illustrated by the problem of constructing a smooth refractor elevation profile from a set of point estimates of the refractor depth.

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