Some extremum problems for matrix norms

1967 ◽  
Vol 7 (2) ◽  
pp. 203-207 ◽  
Author(s):  
V.N. Fadeeva
Keyword(s):  
Extremum Problems ◽  
Matrix Norms

scholarly journals The Global Convergence of the Nonlinear Power Method for Mixed-Subordinate Matrix Norms

2021 ◽  
Vol 88 (1) ◽  
Author(s):  
Antoine Gautier ◽  
Matthias Hein ◽  
Francesco Tudisco
Keyword(s):  
Global Convergence ◽  
Convergence Theorem ◽  
Matrix Norm ◽  
Nonnegative Matrices ◽  
Np Hard ◽  
Power Method ◽  
Contraction Ratio ◽  
Matrix Norms ◽  
Vector Norms

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.

On certain classes of matrix norms

1983 ◽  
Vol 14 (4) ◽  
pp. 357-363
Author(s):  
Massoud Malek-Shahmirzadi ◽  
Kunio Oshima
Keyword(s):  
Matrix Norms

scholarly journals Lower bounds for tau coefficients and operator norms using composite matrix norms

1987 ◽  
Vol 35 (1) ◽  
pp. 49-57
Author(s):  
Choon Peng Tan
Keyword(s):  
Lower Bounds ◽  
General Class ◽  
Special Class ◽  
Operator Norm ◽  
Composite Matrix ◽  
Operator Norms ◽  
Class Of Matrices ◽  
Matrix Norms

Lower bounds for the tau coefficients and operator norms are derived by using composite matrix norms. For a special class of matrices B, our bounds on ‖B‖p (the operator norm of B induced by the ℓp norm) improve upon a general class of Maitre (1967) bounds for p ≥ 2.

scholarly journals Extremum Problems With Total Variation Distance and Their Applications

2014 ◽  
Vol 59 (9) ◽  
pp. 2353-2368 ◽  
Author(s):  
Charalambos D. Charalambous ◽  
Ioannis Tzortzis ◽  
Sergey Loyka ◽  
Themistoklis Charalambous
Keyword(s):  
Total Variation ◽  
Total Variation Distance ◽  
Extremum Problems ◽  
Variation Distance
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