We analyze the global convergence of the power iterates for the computation of a general mixed-subordinate matrix norm. We prove a new global convergence theorem for a class of entrywise nonnegative matrices that generalizes and improves a well-known results for mixed-subordinate \(\ell ^p\) matrix norms. In particular, exploiting the Birkoff–Hopf contraction ratio of nonnegative matrices, we obtain novel and explicit global convergence guarantees for a range of matrix norms whose computation has been recently proven to be NP-hard in the general case, including the case of mixed-subordinate norms induced by the vector norms made by the sum of different \(\ell ^p\)-norms of subsets of entries.

我们分析了计算通用混合从属矩阵范数的幂迭代的全局收敛性。我们为一类入口非负矩阵证明了一个新的全局收敛定理，该定理概括并改进了混合从属\(\ell ^p\)矩阵范数的众所周知的结果。特别是，利用非负矩阵的 Birkoff-Hopf 收缩率，我们获得了一系列矩阵范数的新颖且明确的全局收敛保证，这些范数的计算最近已被证明在一般情况下是 NP-hard 的，包括混合的情况由向量范数引起的从属范数由不同的\(\ell ^p\) -条目子集的范数之和得出。