Fast Methods for Computing the p -Radius of Matrices

The p-radius characterizes the average rate of growth of norms of matrices in a multiplicative semigroup. This quantity has found several applications in recent years. We raise the question of its computability. We prove that the complexity of its approximation increases exponentially with p. We the...

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Bibliographic Details
Published inSIAM journal on scientific computing Vol. 33; no. 3; pp. 1246 - 1266
Main Authors Jungers, Raphaël M., Protasov, Vladimir Y.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2011
Subjects
Accuracy
Approximation
Complexity
Computation
Efficiency
Mathematical analysis
Matrices
Matrix methods
Norms
Studies
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Summary:The p-radius characterizes the average rate of growth of norms of matrices in a multiplicative semigroup. This quantity has found several applications in recent years. We raise the question of its computability. We prove that the complexity of its approximation increases exponentially with p. We then describe a series of approximations that converge to the p-radius with a priori computable accuracy. For nonnegative matrices, this gives efficient approximation schemes for the p-radius computation. [PUBLICATION ABSTRACT]
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ISSN:1064-8275
1095-7197
DOI:10.1137/090777906