ABSTRACT:Sliding polynomials differ from other piecewise interpolation and smoothing methods in their functional continuity at the nodes. This functional continuity was used to establish optional spacing of nodes and optional boundary controls in data smoothing while still maintaining mathematically continuous rates or gradients. Cyclic as well as noncyclic data can be smoothed. Variance of the individual nodal values. derived through least‐squares optimization, can be calculated using the rigorously determined weighting coefficients between data points and nodes. Such nodal variances are estimates of localized uncertainty in the data which complement the localization of smoothing through use of piecewise functions. Choice of controls in smoothing and calculation of variance have been incorporated in a computer program for user convenienc