Challenging eigenvalue perturbation problems
نویسندگان
چکیده
منابع مشابه
Perturbation of Palindromic Eigenvalue Problems
We investigate the perturbation of the palindromic eigenvalue problem for the matrix quadratic P (λ) ≡ λA1 + λA0 + A1, with A0, A1 ∈ Cn×n and A0 = A0. The perturbation of palindromic eigenvalues and eigenvectors, in terms of general matrix polynomials, palindromic linearizations, (semi-Schur) anti-triangular canonical forms, differentiation and Sun’s implicit function approach, are discussed.
متن کاملPerturbation of Partitioned Linear Response Eigenvalue Problems
This paper is concerned with bounds for the linear response eigenvalue problem for H = [ 0 K M 0 ] , where K and M admits a 2 × 2 block partitioning. Bounds on how the changes of its eigenvalues are obtained when K and M are perturbed. They are of linear order with respect to the diagonal block perturbations and of quadratic order with respect to the off-diagonal block perturbations in K and M ...
متن کاملPerturbation Results Related to Palindromic Eigenvalue Problems
We investigate the perturbation of the palindromic eigenvalue problem for the matrix quadratic P(λ)= λ2 A?1 + λA0 + A1 with A0, A1 ∈ C n×n and A?0 = A0 (where ?= T or H ). The perturbation of eigenvalues in the context of general matrix polynomials, palindromic pencils, (semi-Schur) anti-triangular canonical forms and differentiation is discussed. 2000 Mathematics subject classification: primar...
متن کاملPerturbation theory for homogeneous polynomial eigenvalue problems
We consider polynomial eigenvalue problems P(A, α, β)x = 0 in which the matrix polynomial is homogeneous in the eigenvalue (α, β) ∈ C2. In this framework infinite eigenvalues are on the same footing as finite eigenvalues. We view the problem in projective spaces to avoid normalization of the eigenpairs. We show that a polynomial eigenvalue problem is wellposed when its eigenvalues are simple. W...
متن کاملErratum: Perturbation of Partitioned Hermitian Definite Generalized Eigenvalue Problems
The main purpose of this erratum is to correct mistakes in the proof of Theorem 2.4 of [R.-C. Li et al., SIAM J. Matrix Anal. Appl., 32 (2011), pp. 642–663] and in the inequalities (2.23), (2.24), and (2.25) on p. 653 of the same paper.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1998
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)10086-6