A new technique of selection between sequence transformations
There are now many methods for acceleration of the convergence of sequences. However, given a slowly convergent sequence, it can be difficult to determine which convergence acceleration method will be effective. This paper describes a new method for automatically comparing results from different sequence acceleration methods and selecting the best method. The author proves exactness, acceleration, improvement and contraction theorems for the method. Many convergence acceleration methods provide a table of approximations to the sequence limit, where the columns or diagonals of such a table provide infinite families of sequence transformation methods. The author shows how the new selection method can be used for infinite families of methods. The paper concludes with a report about results from several numerical experiments. Example sequences with superlinear convergence, linear convergence, logarithmic convergence and alternating series convergence are used with nine different sequence transformation methods to illustrate the effectiveness of the new transformation selection method.
scientific article; zbMATH DE number 1072312