is published by Princeton University Press and copyrighted, © 2005, by Princeton University Press. All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher, except for reading and browsing via the World Wide Web. Users ar...

It is argued that even for a linear system of ODEs with constant coeecients, stiiness cannot properly be characterized in terms of the eigenvalues of the Jacobian, because stiiness is a transient phenomenon whereas the signiicance of eigenvalues is asymp-totic. Recent theory from the numerical solution of PDEs is adapted to show that a more appropriate characterization can be based upon pseudos...

We describe methods which have been used to analyze the spectrum of non-self-adjoint differential operators, emphasizing the differences from the self-adjoint theory. We find that even in cases in which the eigenfunctions can be determined explicitly, they often do not form a basis; this is closely related to a high degree of instability of the eigenvalues under small perturbations of the opera...

There is more to the computation of pseudospectra than the obvious algorithm of computing singular value decompositions on a grid and sending the results to a contour plotter. Other methods may be hundreds of times faster. The state of the art is reviewed, with emphasis on methods for dense matrices, and a Matlab code is given.

It is argued that even for a linear system of ODEs with constant coefficients, stiffness cannot properly be characterized in terms of the eigenvalues of the Jacobian, because stiffness is a transient phenomenon whereas the significance of eigenvalues is asymptotic. Recent theory from the numerical solution of PDEs is adapted to show that a more appropriate characterization can be based upon pse...

Spectral value sets (SVS) are structured versions of pseudospectra, a tool of matrix analysis that has been popularized by Trefethen and Godunov in recent years. The main result contained in this note is a new algorithm for calculating complex SVS which, using the subharmonicity of the norm of rational matrices, is able to save large amounts of computation whenever the initial set of interest 0...

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...

Using the language of pseudospectra, we study the behavior of matrix eigenvalues under two scales of matrix perturbation. First, we relate Lidskii’s analysis of small perturbations to a recent result of Karow on the growth rate of pseudospectra. Then, considering larger perturbations, we follow recent work of Alam and Bora in characterizing the distance from a given matrix to the set of matrice...

A phenomenon of topological directed amplification certain initial perturbations is revealed theoretically to emerge in a class asymptotically stable skin-effect lattices described by non-normal Toeplitz operators ${H}_{g}$ with positive ``numerical ordinate'' $\ensuremath{\omega}({H}_{g})>0$. Non-normal temporal evolution, even the presence global dissipation, shown manifest counterintuitiv...

The service experts assess the condition of the vehicles based on the produced sound. To benefit both, the riders and the experts, the fault diagnosis process needs to be automated. The paper presents a methodology for fault detection of motorcycles, which uses the slopes of the eight pseudospectral segments as features. The computed features are classified into healthy and faulty using artific...