Some Alternative Methods of Convergence Acceleration

In this work some new nonclassical convergence acceleration concepts are described and compared with the classical convergence acceleration concept. It is shown that these concepts allow to compare the speeds of convergence for a larger set of sequences than the classical convergence acceleration concept. For the acceleration of convergence of sequences regular matrix methods are used. As an application the obtained results can be used for accelerating the convergence of Fourier expansions and for increasing the order of approximation of Fourier expansions and Zygmund means of Fourier expansions in Banach space.