Optimization of Rational Approximations by Continued Fractions
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006. To get guaranteed machine enclosures of a special function f(x), an upper bound ε(f) of the relative error is needed, where ε(f) itself depends on the error bounds ε(app); ε(eval) of the approximation and evaluation error respectively. The approximation function g(x) ≈ f(x) is a rational function (Remez algorithm), and with sufficiently high polynomial degrees...