Topological Analysis of Eigenvalues in Engineering Computations

Melnik, R.V.N.

Engineering Computations, 17(4), 386-416, 2000


The dynamics of coupling between spectrum and resolvent under epsilon-pertubations of operator and matrix spectra ave studied both theoretically and numerically. The phenomenon of non-trivial pseudospectra encountered in these dynamics is treated by relating information in the complex plane to the behaviour of operators and matrices. On a number of numerical results we show how an intrinsic blend of theory with symbolic and numerical computations can be used effectively for the analysis of spectral problems arising from engineering applications.