Perturbation of eigenvalues for periodic matrix pairs via the Bauer–Fike theorems

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Perturbation of eigenvalues for periodic matrix pairs via the Bauer–Fike theorems

In earlier papers, the Bauer–Fike technique was applied to the ordinary eigenvalue problem Ax = λx, the generalized eigenvalue problem Ax = λBx and the matrix polynomial eigenvalue problem ∑m k=0 λAkx = 0. General multiple eigenvalues were dealt with and condition numbers were obtained for individual as well as clusters of eigenvalues. In this paper, we shall generalize the technique to the eig...

متن کامل

On Perturbation Theorems for the Generalized Eigenvalues of Regular Matrix Pairs†

In this paper, we study the Bauer-Fike type theorems for regular matrix pairs and its general form. Besides these, we also obtain some bounds for measuring approximate generalized eigenvalues and for the perturbation of generalized eigenvalues concerning an approximate generalized invariant subspace. To estimate all these bounds, p-Hölder norm and an ad hoc pseudo-metric called p-Chordal matric...

متن کامل

Perturbation analysis for the eigenproblem of periodic matrix pairs

This paper is devoted to perturbation analysis for the eigenproblem of periodic matrix pairs {(Aj ,Ej )}j=1. We first study perturbation expansions of periodic deflating subspaces and eigenvalue pairs. Then, we derive explicit expressions of condition numbers, perturbation bounds and backward errors for eigenvalue pairs and periodic deflating subspaces. © 2001 Elsevier Science Inc. All rights r...

متن کامل

Three Absolute Perturbation Bounds for Matrix Eigenvalues Imply Relative Bounds

We show that three well-known perturbation bounds for matrix eigenvalues imply relative bounds: the Bauer-Fike and Hooman-Wielandt theorems for diagonalisable matrices, and Weyl's theorem for Hermitian matrices. As a consequence, relative perturbation bounds are not necessarily stronger than absolute bounds; and the conditioning of an eigenvalue in the relative sense is the same as in the absol...

متن کامل

Perturbation, Extraction and Refinement of Invariant Pairs for Matrix Polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subs...

متن کامل

ذخیره 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: 2004

ISSN: 0024-3795

DOI: 10.1016/j.laa.2003.06.022