Abstract
Many engineering models, while highly nonlinear globally, are approximately piecewise linear. The linear Shepard algorithm, which is a moving window weighted least squares method based on linear functions, usually creates reasonable approximations. However, when used to produce approximations for data obtained from piecewise linear functions, its performance degrades near the function creases. A better approximation near the function creases can be achieved by using robust estimation algorithms. However, robust estimation algorithms have factorial complexity and require a large number of data points. A robust polynomial-time piecewise linear estimation algorithm has been developed that selects minimal sets of data based on a minimal residual criterion. This algorithm RIPPLE (residual initiated polynomial-time piecewise linear estimation) is shown to produce better approximations than the linear Shepard algorithm.
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