Computationally Efficient Approximations of the Joint Spectral Radius
نویسندگان
چکیده
منابع مشابه
Computationally Efficient Approximations of the Joint Spectral Radius
The joint spectral radius of a set of matrices is a measure of the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from the set. This quantity appears in a number of application contexts but is notoriously difficult to compute and to approximate. We introduce in this paper a procedure for approximating the joint spectral radius of a finite set of m...
متن کاملJoint Spectral Radius : theory and approximations
Acknowledgements I first would like to thank my promotor Vincent Blondel for accepting me as his first Ph.D student, and providing me with a challenging research subject. His constructive comments, his pragmatism and his initiative were essential in the realization of this thesis. Several researchers contributed to this thesis. I would like to especially thank Alexander Vladimirov and Yurii Nes...
متن کاملFast and Precise Approximations of the Joint Spectral Radius
In this paper, we introduce a procedure for approximating the joint spectral radius of a finite set of matrices with arbitrary precision. Our approximation procedure is based on semidefinite liftings and can be implemented in a recursive way. For two matrices even the first step of the procedure gives an approximation, whose relative quality is at least 1/ √ 2, that is, more than 70%. The subse...
متن کاملOn the joint spectral radius
We prove the `p-spectral radius formula for n-tuples of commuting Banach algebra elements. This generalizes results of [6], [7] and [10]. Let A be a Banach algebra with the unit element denoted by 1. Let a = (a1, . . . , an) be an n-tuple of elements of A. Denote by σ(a) the Harte spectrum of a, i.e. λ = (λ1, . . . , λn) / ∈ σ(a) if and only if there exist u1, . . . , un, v1, . . . , vn ∈ A suc...
متن کاملApproximations by Computationally-Efficient VCG-Based Mechanisms
We consider computationally-efficient incentive-compatible mechanisms that use the VCG payment scheme, and study how well they can approximate the social welfare in auction settings. We obtain a 2-approximation for multi-unit auctions, and show that this is best possible, even though from a purely computational perspective an FPTAS exists. For combinatorial auctions among submodular (or subaddi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2005
ISSN: 0895-4798,1095-7162
DOI: 10.1137/040607009