Best Approximation of Positive Power Series
Bruce Shawyer · Mathematics of Computation · 1984
This paper extends work of Fiedler, Jurkat and the present author to series of the form $\Sigma {a_n}{x^n}$ where $\{ {a_n}\}$ is a moment sequence and $0 < x < 1$. In the cases where it is possible to calculate it exactly, we find the best ${L^p}$ approximation to the sum of the series and the actual terms of the matrices involved. We have an advantage over accelerators commonly used for accelerating convergence in that we know explicitly the errors in our calculations.