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Manuscript Title: Numerical generation and use of orthonormal polynomials I. ORT1 - a one-dimensional package for the solution of fitting, differentiation and integration problems.
Authors: V. Gadjokov, J. Jordanova
Program title: ORT1 POLYNOMIAL FIT DIFF/INT
Catalogue identifier: ACFM_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 31(1984)53
Programming language: Fortran.
Computer: IBM 370/145.
Operating system: OS/VS.
RAM: 17K words
Word size: 32
Keywords: General purpose, Global polynomial, Fit, Noise, Recursive Orthonormalization, Optimum matrix condition, Telescoping, Differentiation, Error estimation.
Classification: 4.9.

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.

Restrictions:
Up to 200 points to fit by means of polynomial series not exceeding the 25-th degree. These limits may be enlarged by introducing higher dimensions of the working-memory arrays.

Unusual features:
Absence of iteration and matrix-inversion procedures.