Smoothing and Estimation Derivatives of Equispaced Data

This paper discusses various aspects of the smoothing and estimation of derivatives of equispaced data. The background for least squares polynomial smoothing is summarized . The various alternatives for programs in a computing center ' s library are discussed and a part icular alternative is selected as most sui table. An algorithm named SMOOTH is given [in Fortran) which implements this al ternat ive. SMOOTH estimates the smoothed value of the data or its first or second derivative based on specified polynomial degree and nunber of points to enter the smoothing . The paper concludes wi th a discussion of methods sui table to compute large arrays of smoothing weights . There are 3 appendices which contain , respect ively , expl ici t formulas associated wi th Gram polynomials, expl icit formulas for the smoothing weights and tables of initial segments of arrays for computing large tables of smoothing weights .