Fast least‐squares algorithms Available to Purchase

New least‐squares algorithms are introduced. Instead of waiting for all data to be in before making a fit, these algorithms update a fit after each point is entered so trends can be detected promptly as an experiment proceeds. Coupled linear equations are not solved numerically, reducing rounding errors, calculation time, and memory requirements. When used for fitting degree‐N polynomials to equally weighted data points whose abscissas are equally spaced, these algorithms need just one multiplication by an integer constant and one division to update each of the N+1 polynomial coefficients. Pocket calculator programs are available for polynomial fits to data points whose abscissas are equally spaced; one of these gives equal weight to all points while another gives more weight to recent points.