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Regular version of the site

Article

Optimizing the spactral radius

SIAM Journal on Matrix Analysis and Applications. 2013. Vol. 34. No. 3. P. 999-1013.

We suggest a new approach to finding the maximal and the minimal spectral radii of linear operators from a given compact family of operators, which share a common invariant cone (e.g., family of nonnegative matrices). In the case of families with the so-called product structure, this leads to efficient algorithms for optimizing the spectral radius and for finding the joint and lower spectral radii of the family. Applications to the theory of difference equations and to problems of optimizing the spectral radius of graphs are considered.