Convergence of Infinite Products of Matrices and Inner–outer Iteration Schemes∗
نویسنده
چکیده
Abstract. We develop conditions under which a product ∏∞ i=0 Ti of matrices chosen from a possibly infinite set of matrices S = {Tj |j ∈ J} converges. We obtain the following conditions which are sufficient for the convergence of the product: There exists a vector norm such that all matrices in S are nonexpansive with respect to this norm and there exists a subsequence {ik}k=0 of the sequence of the nonnegative integers such that the corresponding sequence of operators { Tik }∞
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