Numerical generation and use of orthonormal polynomials: I. ORT1— A one-dimensional package for the solution of fitting, differentiation and integration problems. Nature of problem: An approach to smooth polynomial fitting of experimental data which contain noise is presented. The problem of calibrating nonlinear measuring devices may be considered as a typical, although far from unique, representative of possible physical applications. Solution method: A generalized recurrence of the Forsythe’s type is used to achieve: (a) optimum condition of matrices involved which allows for high-degree fits in single-precision arithmetics; (b) fast and accurate telescoping of orthonormal polynomial fitting series; (c) stable computation of derivatives and integrals of fitting series as well as of the respective error corridors.

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  1. Bogdanova, N.B.: Orthonormal polynomials in one and two dimensions: application to calibration problems in high energy physics (1986)