Perturbation effects in nonlinear eigenvalue problems

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.

Nonlinear Eigenvalue Problems

Heinrich Voss Hamburg University of Technology 115.1 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115-2 115.2 Analytic matrix functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115-3 115.3 Variational Characterization of Eigenvalues . . . . . . . . 115-7 115.4 General Rayleigh Functionals . . . . . . . . . . . . . . . . . . . ...

Solving nonlinear eigenvalue problems

Perturbation 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 ...

Perturbation 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...