In a recent paper, we constructed a stationary 1−dependent 4−coloring of the integers that is invariant under permutations of the colors. This was the first stationary finitely dependent q−coloring for any q. When the analogous construction is carried out for q > 4 colors, the resulting process is not finitely dependent. We construct here a process that is symmetric in the colors and 1−dependen...

The problem of calculating the best approximating straight line--in the sense of Chebyshev--to a finite set of points in R" is considered. Firstand second-order optimality conditions are derived and analysed. Lipschitz optimization techniques can be used to find a global minimizer.

The aim of this paper is to improve the convergence rate of frame algorithm based on Richardson iteration and Chebyshev methods. Based on Richardson iteration method, we first square the existing convergence rate of frame algorithm which in turn the number of iterations would be bisected and increased speed of convergence is achieved. Afterward, by using Chebyshev polynomials, we improve this s...