2012/01/16 by Vladimir Yu. Protasov, Raphaël M. Jungers, Protasov, Vladimir Yu. +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Mathematics #Gene Regulatory Network Analysis #Graph theory and applications #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1201.3218
openalex publication_date 2012/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new approach to evaluate the largest Lyapunov exponent of a\nfamily of nonnegative matrices. The method is based on using special positive\nhomogeneous functionals on Rd+, which gives iterative lower and upper\nbounds for the Lyapunov exponent. They improve previously known bounds and\nconverge to the real value. The rate of convergence is estimated and the\nefficiency of the algorithm is demonstrated on several problems from\napplications (in functional analysis, combinatorics, and lan- guage theory) and\non numerical examples with randomly generated matrices. The method computes the\nLyapunov exponent with a prescribed accuracy in relatively high dimensions (up\nto 60). We generalize this approach to all matrices, not necessar- ily\nnonnegative, derive a new universal upper bound for the Lyapunov exponent, and\nshow that such a lower bound, in general, does not exist.\n