Algebraic multilevel iteration methods and the best approximation to $1/x$ in the uniform norm

Details Algebraic multilevel iteration methods and the best approximation to $1/x$ in the uniform norm Algebraic multilevel iteration methods and the best approximation to $1/x$ in the uniform norm

2010-02-09

arxiv.org/abs/1002.1859v1

Mathematics

Numerical Analysis

Tech report Ricam

Scientific paper

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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