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A number of renormalization schemes for improving the convergence of multiple scattering series expansions are investigated. Numerical tests on a small Cu(111) cluster demonstrate their effectiveness, for example increasing the rate of convergence by up to a factor 2 or by transforming a divergent series into a convergent one. These techniques can greatly facilitate multiple scattering calculations, especially for spectroscopies such as photoelectron diffraction, Auger electron diffraction, low energy electron diffraction etc., where an electron propagates with a kinetic energy of hundreds of eV in a cluster of hundreds of atoms. [ABSTRACT FROM AUTHOR]