Abstract
We analyze the computability and the complexity of various definitions of spectral radii for sets of matrices. We show that the joint and generalized spectral radii of two integer matrices are not approximable in polynomial time, and that two related quantities—the lower spectral radius and the largest Lyapunov exponent—are not algorithmically approximable.
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This work was completed while Blondel was visiting Tsitsiklis at MIT. This research was supported by the ARO under Grant DAAL-03-92-G-0115.
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Tsitsiklis, J.N., Blondel, V.D. The Lyapunov exponent and joint spectral radius of pairs of matrices are hard—when not impossible—to compute and to approximate. Math. Control Signal Systems 10, 31–40 (1997). https://doi.org/10.1007/BF01219774
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DOI: https://doi.org/10.1007/BF01219774