A set \({\mathcal S}\) of convergent sequences is said to be accelerable if there is a sequence transformation T such that \(\lim_{n\to \infty}(T_ n-S)/(S_ n-S)=0\text{ for any} (S_ n)\in {\mathcal S},\) where S is the limit of \((S_ n)\) and \((T_ n)=T(S_ n)\). A real sequence \((S_ n)\) converging to S is said to be a logarithmic sequence if \(\lim_{n\to \infty}(S_{n+1}-S)/(S_ n-S)=1.\) We denote by LOG the set of all logarithmic sequences. We denote by LOGSF the set of all logarithmic sequences satisfying \(\lim_{n\to \infty}\Delta S_{n+1}/\Delta S_ n=1,\) where \(\Delta S_ n=S_{n+1}-S_ n.\)
The aim of this paper is to study what the accelerable subsets of LOGSF of all logarithmically convergent sequences are. Three kinds of subsets of LOGSF and sequence transformations as well as numerical examples are given.