The nearest definite pair for the Hermitian generalized eigenvalue problem
نویسندگان
چکیده
منابع مشابه
The nearest de®nite pair for the Hermitian generalized eigenvalue problem
The generalized eigenvalue problem Ax kBx has special properties when A;B is a Hermitian and de®nite pair. Given a general Hermitian pair A;B it is of interest to ®nd the nearest de®nite pair having a speci®ed Crawford number d > 0. We solve the problem in terms of the inner numerical radius associated with the ®eld of values of A iB. We show that once the problem has been solved it is t...
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15 صفحه اولErratum: Perturbation of Partitioned Hermitian Definite Generalized Eigenvalue Problems
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متن کاملPerturbation of Partitioned Hermitian Definite Generalized Eigenvalue Problems
This paper is concerned with the Hermitian definite generalized eigenvalue problem A− λB for block diagonal matrices A 1⁄4 diagðA11; A22Þ and B 1⁄4 diagðB11; B22Þ. Both A and B are Hermitian, and B is positive definite. Bounds on how its eigenvalues vary when A and B are perturbed by Hermitian matrices are established. These bounds are generally of linear order with respect to the perturbations...
متن کاملPerturbation 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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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1999
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(99)00026-9