The sign regularity of the auxiliary family g_i(x) = x(~αi)(-ln x)~(βi) in convergence acceleration processes using the E-algorithm

摘要

The E-algorithm can be successfully applied to accelerate the convergence of the solution of some numerical differential equations provided the respective error expansion satisfies a certain asymptotic determinantal condition. In this work it is proved that such condition is fulfilled for any error expansion in which formation enter the auxiliary family hni(?lnhn)i (where hn designates the stepsize of the discretization method).