New Methods for Accelerating the Convergence of Sequences Arising in Laplace Transform Theory
Jet Wimp · SIAM Journal on Numerical Analysis · 1977
We discuss a new class of linear summation methods which are highly effective in accelerating the convergence of sequences which can be represented by Laplace moment integrals with generating function $f(t)$. Different formulas are obtained corresponding to different $L_p^r $ classes for f. The methods are shown to be nonregular, but for the sequences studied they do preserve convergence and are generally much more efficient than the usual regular methods. We provide simple error bounds. We close with criteria which should help the reader to decide when a given sequence is a likely candidate for a successful application of these methods.