An algorithm for Chebyshev approximation by rationals with constrained denominators

The problem of rational approximation is facilitated by introducing both lower and upper bounds on the denominators. For a general fractional inf-sup problem with constrained denominators, a differential correction algorithm and convergence results are given. Numerical examples are presented. The proposed algorithm has certain advantages compared with the original differential correction method: not only upper but also lower bounds for the optimal value are computed, linear convergence is always guaranteed, and due to a different start convergence is more rapid.