A METHOD OF DESCENT FOR CHEBYSHEV APPROXIMATION.
LUND UNIV (SWEDEN) INST OF COMPUTER SCIENCES
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A procedure is developed for the calculation of a best Chebyshev approximation among linear combinations of given continuous functions phi sub zero, phi sub 1, ..., phi sub N, to a continuous function in a compact interval. The procedure uses a descent method to minimize the Chebyshev norm of the error function. In some cases the choice of direction of descent resembles an idea developed by Zuhovickii for discrete approximations. However, in general, a different way to calculate this direction is used. This choice of direction, made in an adaptive manner, makes it possible to work with an easily determined estimate of the stepsize. Even with very bad initial values the given method converges. It is easily extended to the case when the approximating functions do not fulfil the Haar condition. The effectiveness is illustrated with numerical examples. Author
- Theoretical Mathematics