Matrix analysis
Two-scale difference equations II. local regularity, infinite products of matrices and fractals
SIAM Journal on Mathematical Analysis
Characterizations of Scaling Functions: Continuous Solutions
SIAM Journal on Matrix Analysis and Applications
Computationally Efficient Approximations of the Joint Spectral Radius
SIAM Journal on Matrix Analysis and Applications
On the number of α-power-free binary words for 2
Theoretical Computer Science
Overlap-free words and spectra of matrices
Theoretical Computer Science
On codes that avoid specified differences
IEEE Transactions on Information Theory
On the Complexity of Computing the Capacity of Codes That Avoid Forbidden Difference Patterns
IEEE Transactions on Information Theory
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We propose two simple upper bounds for the joint spectral radius of sets of nonnegative matrices. These bounds, the joint column radius and the joint row radius, can be computed in polynomial time as solutions of convex optimization problems. We show that these bounds are within a factor $1/n$ of the exact value, where $n$ is the size of the matrices. Moreover, for sets of matrices with independent column uncertainties or with independent row uncertainties, the corresponding bounds coincide with the joint spectral radius. In these cases, the joint spectral radius is also given by the largest spectral radius of the matrices in the set. As a by-product of these results, we propose a polynomial-time technique for solving Boolean optimization problems related to the spectral radius. We also describe economics and engineering applications of our results.