Stability of the linear inequality method for rational Chebyshev approximation (Q1067351)

Given \(\epsilon\) \(\to 0\) and a function f, the author studies the problem of finding a rational function \(p_{\epsilon}/q_{\epsilon}\) of order (m,n) such that -\(\epsilon\) q(x)\(\leq f(x)q(x)-p(x)\leq \epsilon q(x)\). He proves a convergence theorem for \(\{p_{\epsilon}/q_{\epsilon}\}\) letting \(\epsilon\) to tend to the minimal admissible value.