Acceleration methods for vector sequences (Q1184134)

The purpose of this paper is to propose acceleration methods for certain logarithmic vector sequences. These methods are obtained by extending acceleration methods for scalar logarithmic sequences: Lubkin's \(W\) transform, the \(\theta\)-algorithm and the \(\rho\)-algorithm. Such methods accelerate certain logarithmically convergent vector sequences. However, the vector \(\delta\)-algorithm and the minimal polynomial extrapolation scarcely accelerate such vector sequences. To the author's opinion, all of the \(W\) transforms and the \(\theta\)- algorithms work well on not only certain logarithmically convergent vector sequences, but also on linearly convergent vector sequences. Numerical results showing that acceleration methods are useful for finding zeros of singular equations are given. Extrapolation theorems and error analysis of the new acceleration methods represent future research topics of the author.