In different fields in space researches, Scientists are in need to deal with the product of matrices. In this paper, we develop conditions under which a product Пi=0∞ of matrices chosen from a possibly infinite set of matrices M={Pj, j∈J} converges. There exists a vector norm such that all matrices in M are no expansive with respect to this norm and also a subsequence {ik}k=0∞ of the sequence of nonnegative integers such that the corresponding sequence of operators {Pik}k=0∞ converges to an operator which is paracontracting with respect to this norm. The continuity of the limit of the product of matrices as a function of the sequences {ik}k=0∞ is deduced. The results are applied to the convergence of inner-outer iteration schemes for solving singular consistent linear systems of equations, where the outer splitting is regular and the inner splitting is weak regular.
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机译：在太空研究的不同领域，科学家需要处理矩阵乘积。在本文中，我们开发了一个条件，在该条件下，从可能无限的矩阵集合M = {Pj，j∈J}中选择的矩阵乘积Пi=0∞收敛。存在一个向量范数，使得M中的所有矩阵都相对于该范数不扩张，并且还存在非负整数序列的子序列{ik} k =0∞，从而对应的算子序列{Pik} k =0∞会聚到与该规范有合同关系的运营商。推导了矩阵乘积的极限的连续性，取决于序列{ik} k =0∞。将结果应用于内外迭代方案的收敛性，以求解奇异的一致线性方程组，其中外分裂是规则的，而内分裂是弱规则的。
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