Algebraic multilevel iteration methods and the best approximation to $1/x$ in the uniform norm. (arXiv:1002.1859v1 [math.NA])

Algebraic multilevel iteration methods and the best approximation to $1/x$ in the uniform norm. (arXiv:1002.1859v1 [math.NA]): "

In this note, we provide simple convergence analysis for the algebraic
multilevel iteration methods. We consider two examples of AMLI methods with
different polynomial acceleration. The first one is based on shifted and scaled
Chebyshev polynomial and the other on the polynomial of best approximation to
$x^{-1}$ on a finite interval with positive endpoints in the uniform norm. The
construction of the latter polynomial is of interest by itself, and we have
included a derivation of a 3 term recurrence relation for computing this
polynomial. We have also derived several inequalities related to the error of
best approximation, which we applied in the AMLI analysis.

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