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Yayın Some notes on improvement of convergence by regular matrices(Maltepe Üniversitesi, 2009) Aasma, AntsWe consider some aspects of convergence acceleration by regular matrices M = (mnk) with real or complex entries. Classically a matrix M is called accelerating the convergence if the relation holds for every convergent sequence x = (xn) . Besides the classical concept of comparing and estimating the speeds of convergence of sequences and series we use weakened criterion, called improvement of convergence ([1]). As an application regular matrices are used for increasing the order of approximation of Fourier expansions and Zygmund means of Fourier expansions in certain Banach spaces.