منابع مشابه
Pseudospectral Components and the Distance to Uncontrollability
We show that 2-norm pseudospectra ofm-by-nmatrices have no more than 2m(4m−1) connected components. Such bounds are pertinent for computing the distance to uncontrollability of a control system, since this distance is the minimum value of a function whose level sets are pseudospectra. We also discuss algorithms for computing this distance, including a trisection variant of Gu’s recent algorithm...
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This article is concerned with the structured distance to uncontrollability of a linear time-invariant system and relates this concept to a variation of the μ-value. The developed framework is applied to derive computational expressions for the class of real perturbations as well as for Hermitian, symmetric, and skew-symmetric perturbations in a relatively simple manner. Examples demonstrate th...
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This paper reports on two studies which investigated the relationship between children’s texting behaviour, their knowledge of text abbreviations and their school attainment in written language skills. In Study One, 11–12-year-old children provided information on their texting behaviour. They were also asked to translate a standard English sentence into a text message and vice versa. The childr...
متن کاملQualitative Controllability and Uncontrollability by a Single Entry
We characterize matrices A ∈ Cn×n whose zero/nonzero pattern requires that the controllability matrix [b Ab Ab . . . An−1b] ∈ Cn×n is of full rank, where b ∈ Cn×1 has exactly one nonzero entry. When all the diagonal entries of A are nonzero we show that this occurs if and only if QAQ is unreduced upper Hessenberg, with Q being a permutation matrix for which Qb = [b1, 0, . . . , 0] T . We also c...
متن کاملDeflation in Krylov Subspace Methods and Distance to Uncontrollability
The task of extracting from a Krylov decomposition the approximation to an eigenpair that yields the smallest backward error can be phrased as finding the smallest perturbation which makes an associated matrix pair uncontrollable. Exploiting this relationship, we propose a new deflation criterion, which potentially admits earlier deflations than standard deflation criteria. Along these lines, a...
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ژورنال
عنوان ژورنال: Reading Research Quarterly
سال: 2021
ISSN: 0034-0553,1936-2722
DOI: 10.1002/rrq.387