Programs in Physics & Physical Chemistry
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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.|
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.
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.
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.
Absence of iteration and matrix-inversion procedures.
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