Adaptive monotone rational approximation on finite sets (Q1870260)

The problem of uniform approximation on a finite set of real numbers by rational functions whose first derivative is required to be positive (negative) and denominator is required to be positive on the smallest interval containing the points is considered. An earlier nonadaptive computational code is now extended to the present adaptive code by coupling it with a positivity checker for polynomials on intervals developed herein. This new code allows for an intelligent selection of additional constraining points beyond the initial data points to enforce monotonicity preserving pole free fits to monotone data sets. In addition, it also provides the option of enforcing pole-free fits while ignoring monotonicity.