Fast Methods for Computing the $p$-Radius of Matrices
Name
Jungers-2011-FAST METHODS FOR COMPUTING THE.pdf
Size
324.19 KB
Format
Adobe PDF
Checksum (MD5)
e0067e27c0c64a1e14ec8f0afbf3c8dc
Author(s)
Jungers, Raphael M.
Protasov, Vladimir Y.
Date Issued
June 2011
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Jungers, Raphaël M., and Vladimir Y. Protasov. “Fast Methods for Computing the $p$-Radius of Matrices.” SIAM Journal on Scientific Computing 33.3 (2011) : 1246. © 2011 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/090777906
