Perturbation thèorems for the generalized eigenvalue problem
نویسندگان
چکیده
منابع مشابه
Perturbation of Partitioned Hermitian Generalized Eigenvalue Problem
We are concerned with the perturbation of a multiple eigenvalue μ of the Hermitian matrix A = diag(μI,A22) when it undergoes an off-diagonal perturbation E whose columns have widely varying magnitudes. When some of E’s columns are much smaller than the others, some copies of μ are much less sensitive than any existing bound suggests. We explain this phenomenon by establishing individual perturb...
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15 صفحه اولThe Generalized Eigenvalue Problem for Nonsquare Pencils Using a Minimal Perturbation Approach
This work focuses on non-square matrix pencils A − λB where A,B ∈ Mm×n and m > n. Traditional methods for solving such nonsquare generalized eigenvalue problems (A−λB)v = 0 are expected to lead to no solutions in most cases. In this paper we propose a different treatment; We search for the minimal perturbation to the pair (A,B) such that these solutions are indeed possible. Two cases are consid...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1982
ISSN: 0024-3795
DOI: 10.1016/0024-3795(82)90120-3