Istituto di Matematica Applicata e Tecnologie Informatiche     
Simoncini V. Non-linear spectral perturbation: A qualitative analysis. Preprint ercim.cnr.ian//1997-1032, 1997.
We are interested in the analysis of nonlinear perturbation effects in the spectrum of a real nonsymmetric matrix $A$ under linear perturbations. We discuss some known results and we use them to justify some recent experimental observations. The qualitative behavior of the eigenvalues of $A$ under large perturbations is not only predicted by inspecting the resolvent norm of $A$ but by also evaluating the spectral radius of a related matrix. We show how to numerically compute this radius for large matrices and how this information can be used to analyze the quality of the approximation of a projection method and to detect the presence of spurious approximate eigenvalues
Subject 65-XX

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