Abstract:
A new iterative method for finding the parameters of polynomials of best approximation with weight in
$C[-1,1]$ is presented. It is based on the representation of the error in the trigonometric form in terms of the phase function. The iterative method of finding the corrections to the phase functions that determine
the joint motion of the zeros and the $e$-points of the error is based on inverse analysis, perturbation theory, and asymptotic formulae for extremal polynomials.
Bibliography: 24 titles.
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