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On the Lidskii--Vishik--Lyusternik Perturbation Theory for Eigenvalues of Matrices with Arbitrary Jordan Structure
Let A be a complex matrix with arbitrary Jordan structure and $\lambda$ an eigenvalue of A whose largest Jordan block has size n. We review previous results due to Lidskii [U.S.S. R. Comput. Math.Expand
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Structured Hölder Condition Numbers for Multiple Eigenvalues
TLDR
The sensitivity of a multiple eigenvalue of a matrix under perturbations can be measured by its Holder condition number. Expand
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Low Rank Perturbation of Jordan Structure
  • J. Moro, F. Dopico
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 1 February 2003
TLDR
We show that for most matrices B satisfying ${\rm rank}\,(B)\leq g$, the Jordan blocks of A+B with eigenvalue $\lambda_0$ are just the smallest Jordan blocks in the Jordan canonical form of A, while the rest remain unchanged. Expand
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Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices
We present a Weyl-type relative bound for eigenvalues of Hermitian perturbations A+E of (not necessarily definite) Hermitian matrices A. This bound, given in function of the quantityExpand
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First order spectral perturbation theory of square singular matrix pencils
Abstract Let H ( λ ) = A 0 + λ A 1 be a square singular matrix pencil, and let λ 0 ∈ C be an eventually multiple eigenvalue of H ( λ ) . It is known that arbitrarily small perturbations of H ( λ )Expand
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Low Rank Perturbation of Weierstrass Structure
TLDR
We show that for most matrices $B_0 + \lambda_0 B_1$ with ${\rm rank} in the Weierstrass canonical form, there are Jordan blocks corresponding to the eigenvalue of the perturbed pencil $A_0+A_1+B_1$. Expand
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Lagrangian means
Abstract. We define Lagrangian means as those obtained from applying the classical mean value formula to a strictly convex regular function. We show that there is a close relationship betweenExpand
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Accurate Factorization and Eigenvalue Algorithms for Symmetric DSTU and TSC Matrices
TLDR
Two algorithms are presented which compute, with small componentwise relative error, a block $LDL^T$ factorization of symmetric matrices belonging to two classes of matrices: diagonally scaled totally unimodular (DSTU) and total signed compound matrices. Expand
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On nonnegative matrices similar to positive matrices
Abstract Let Nn denote the set of those (1, λ2, …, λn) ∈ C n such that there exists a nonnegative matrix with Perron root equal to one and spectrum {1, λ2, …, λn}. We prove that Nn is star-shapedExpand
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On the distributional Fourier duality and its applications
Abstract Sampling theorems for bandlimited functions or distributions are obtained by exploiting the topological isomorphism between the space E ′( R ) of distributions of compact support on R andExpand
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