On the stability of a class of convergence acceleration methods for power series
Power series having the form \(F(z)=\sum^{\infty}_{r=0}z^ rf_ rc_ r\) are studied where z is a complex number, and assuming i) F has a positive radius of convergence R. ii) \(f(z)=\sum^{\infty}_{r=0}z^ rf_ r,\) is known as analytical expression, and iii) \(c_ r=\int^{b}_{a}t^ rd\alpha (t),\) \(\alpha\) of bounded variation on [a,b] and independent of r. The results obtained are applied to the problem of evaluating the sum of a power series whose terms are given numerically with moderate accuracy. The sum is approximated using values of a finite number of terms. The stability of the process is discussed. A result on the stability of product quadrature rules is also given.
scientific article; zbMATH DE number 3879970