Smoothing and estimating derivatives of equispaced data†

This paper discusses various aspects of the smoothing and estimation of derivatives of equispaced data using least squares and polynomials. The various alternatives for programs in a computing center's library are discussed and a particular alternative is selected as most suitable. An algorithm named SMOOTH is given (in Fortran) which implements this alternative. SMOOTH estimates the smoothed value of the data or its first or second derivative based on specified polynomial degree and number of points to enter the smoothing. The paper concludes with a discussion of methods suitable to compute large arrays of smoothing weights