The Global Convergence of the Nonlinear Power Method for Mixed-Subordinate Matrix Norms
Keyword(s):
Np Hard
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AbstractWe 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 $$\ell ^p$$ ℓ 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 $$\ell ^p$$ ℓ p -norms of subsets of entries.
1990 ◽
Vol 97
(5)
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pp. 406-407
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2016 ◽
Vol 94
(3)
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pp. 411-420
2010 ◽
Vol 14
(3B)
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pp. 1135-1144
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1996 ◽
Vol 33
(4)
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pp. 1559-1576
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