The behavior of the vector recurrence yn+1 = Myn + wn+1 is studied under very weak assumptions. Let λ(M) denote the spectral radius of M and let X(M)≥1. Then if the wn are bounded in norm and a certain subspace hypothesis holds, the root order of the yn is shown to be λ(M). If one additional hypoth¬esis on the dimension of the principal Jordan blocks of M holds, then the quo¬tient order of the yn is also λ(M). The behavior of the homogeneous recurrence is studied for all values of λ(M).nThese results are applied to the analysis ofn(1) Nonlinear iteration with application to iteration with memory and to parallel iteration algorithmsn(2) Order and efficiency of composite iterationn(3) The power method.
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