Titlebook: Recent Advances in Matrix and Operator Theory; Joseph A. Ball,Yuli Eidelman,James Rovnyak Conference proceedings 2008 Birkhäuser Basel 200

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A Fast QR Algorithm for Companion Matrices,asing is done on the SSS form QR factors of the Hessenberg iterates. Both double shift and single shift versions are provided. Deflation and balancing are also discussed. Numerical results are presented to illustrate both high efficiency and numerical robustness of the new QR algorithm.

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Stability of Dynamical Systems via Semidefinite Programming, where A is a positive definite real matrix. Our search for Lyapunov functions is based on interior point algorithms for solving certain positive definite programming problems and is applicable for non-polynomial systems not considered by similar methods earlier.

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A Fast QR Algorithm for Companion Matrices,ch invariant rank structures were exploited therein to design fast QR iteration algorithms for finding eigenvalues of companion matrices. These algorithms require only O(.) storage and run in O(n.) time where . is the dimensiosn of the matrix. In this paper, we propose a new O(n.) complexity QR algo

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A Perturbative Analysis of the Reduction into Diagonal-plus-semiseparable Form of Symmetric Matricewith prescribed diagonal term. In this paper, we present perturbation bounds for such transformations, under the condition that the diagonal term is close to (part of) the spectrum of the given matrix. As an application, we provide new iterative schemes for the simultaneous refinement of the eigenva

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The Eigenstructure of Complex Symmetric Operators,mmetric operators. In particular, we examine the relationship between the bilinear form [. induced by a conjugation . on a complex Hilbert space . and the eigenstructure of a bounded linear operator T: . which is .-symmetric . = .

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,Higher Order Asymptotic Formulas for Traces of Toeplitz Matrices with Symbols in Hölder-Zygmund Spa in this formula goes to zero very rapidly for very smooth symbols. This formula refines previous asymptotic trace formulas by Szegő and Widom and complement higher order asymptotic formulas for determinants of finite block Toeplitz matrices due to Böttcher and Silbermann.