Topological analysis of eigenvalues in engineering computations

The dynamics of coupling between spectrum and resolvent under epsilon-pertu bations of operator and matrix spectra ave studied both theoretically and n umerically. The phenomenon of non-trivial pseudospectra encountered in thes e dynamics is treated by relating information in the complex plane to the b ehaviour of operators and matrices. On a number of numerical results we sho w 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.