Abstract:
In this paper, we study the relationships between the best uniform polynomial approximations of a continuous function on an interval and its even and odd prolongations. We consider examples that demonstrate the accuracy of the results obtained. Similar issues are also discussed for rational approximations.
Keywords:best uniform polynomial approximation, best uniform rational approximation, even continuation of a function, odd continuation of a function, Jackson's inequality.
Fulltext:
PDF file (192 kB)