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Regular version of the site
Of all publications in the section: 5
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Article
Protasov V. Y. SIAM Journal on Matrix Analysis and Applications. 2013. Vol. 34. No. 3. P. 1174-1188.
Article
Protasov V. Y., Guglielmi N. SIAM Journal on Matrix Analysis and Applications. 2016. Vol. 37. No. 1. P. 18-52.

We generalize the recent invariant polytope algorithm for computing the joint spectral radius and extend it to a wider class of matrix sets. This, in particular, makes the algorithm applicable to sets of matrices that have finitely many spectrum maximizing products. A criterion of convergence of the algorithm is proved. As an application we solve two challenging computational open problems. First we find the regularity of the Butterfly subdivision scheme for various parameters $\omega$. In the “most regular” case $\omega = \frac{1}{16}$, we prove that the limit function has Holder exponent 2 and its derivative is “almost Lipschitz” with logarithmic factor 2. Second we compute the Holder exponent of Daubechies wavelets of high order.

Article
Nesterov Y., Protasov V. Y. 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.