Chebyshev system; extremal points; iterative algorithm; Chebyshev approximations; numerical examples; $Q$-order of a convergent iterative method
The paper gives such an iterative method for special Chebyshev approxiamtions that its order of convergence is $\geq 2$. Somewhat comparable results are found in  and , based on another idea.
 K. Glasshoff S. A. Gustafson: Linear Optimization and Approximation
. Springer-Verlag, New York, 1983. MR 0697234
 F. Kálovics: An agorithm for best Chebyshev approxmations
. Annales. Univ. Sci. Budapestinensis, Sectio Computatorica, 6(1985), 19-25. MR 0915220
 J. M. Ortega W. C. Rheinboldt: Iterative Solutions of Nonlinear Equations in Several Variables
. Academic Press, New York, 1970. MR 0273810