Structured Pseudospectra, Μ-values and Eigenvalue Condition Numbers (summary of Cumulative Habilitation)

نویسندگان

  • MICHAEL KAROW
  • Eugene Gutkin
  • Edmond Jonckheere
  • Michael Karow
  • Diederich Hinrichsen
  • Anthony J. Pritchard
  • Daniel Kressner
  • Francoise Tisseur
  • M. KAROW
چکیده

where B ∈ C, C ∈ C are fixed matrices and ∆ is an element of a subset ∆ of C. It is assumed that ∆ is closed, connected and contains the zero matrix. The size of a perturbation ∆ ∈ ∆ is measured by a norm ‖ · ‖ on C. (a) The structued pseudospectrum (also called spectral value set) of the triple (A,B,C) with respect to the perturbation class ∆, the underlying norm ‖ · ‖ and the perturbation level δ > 0 is defined as

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Structured Pseudospectra for Small Perturbations

In this paper we study the shape and growth of structured pseudospectra for small matrix perturbations of the form A A∆ = A + B∆C, ∆ ∈ ∆, ‖∆‖ ≤ δ. It is shown that the properly scaled pseudospectra components converge to non-trivial limit sets as δ tends to 0. We discuss the relationship of these limit sets with μ-values and structured eigenvalue condition numbers for multiple eigenvalues.

متن کامل

On the computation of structured singular values and pseudospectra

Structured singular values and pseudospectra play an important role in assessing the properties of a linear system under structured perturbations. This paper discusses computational aspects of structured pseudospectra for structures that admit an eigenvalue minimization characterization, including the classes of real, skew-symmetric, Hermitian, and Hamiltonian perturbations. For all these struc...

متن کامل

Several Concepts to Investigate Strongly Nonnormal Eigenvalue Problems

Eigenvalue analysis plays an important role in understanding physical phenomena. However, if one deals with strongly nonnormal matrices or operators, the eigen-values alone may not tell the full story. A popular tool which can be useful to get more insight in the reliability or sensitivity of eigenvalues is "-pseudospectra. Apart from "-pseudospectra we consider other tools which might help to ...

متن کامل

Backward errors and pseudospectra for structured nonlinear eigenvalue problems

Minimal structured perturbations are constructed such that an approximate eigenpair of a nonlinear eigenvalue problem in homogeneous form is an exact eigenpair of an appropriately perturbed nonlinear matrix function. Structured and unstructured backward errors are compared. These results extend previous results for (structured) matrix polynomials to more general functions. Structured and unstru...

متن کامل

Eigenvalue condition numbers and Pseudospectra of Fiedler matrices

The aim of the present paper is to analyze the behavior of Fiedler companion matrices in the polynomial root-finding problem from the point of view of conditioning of eigenvalues. More precisely, we compare: (a) the condition number of a given root λ of a monic polynomial p(z) with the condition number of λ as an eigenvalue of any Fiedler matrix of p(z), (b) the condition number of λ as an eige...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008