We present new theoretical results on two classes of multisplitting methods for solving linear systems iteratively. These classes are based on overlapping blocks of the underlying coefficient matrix \( A \) which is assumed to be a band matrix. We show that under suitable conditions the spectral radius \( \rho(H) \) of the iteration matrix \( H \) does not depend on the weights of the method even if these weights are allowed to be negative. For a certain class of splittings we prove an optimality result for \( \rho(H) \) with respect to the weights provided that \( A \) is an M–matrix. This result is based on the fact that the multisplitting method can be represented by a single splitting \( A = M - N \) which in our situation surprisingly turns out to be a regular splitting. Furthermore we show by numerical examples that weighting factors \( \alpha \not \in [0,1] \) may considerably improve the convergence.
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