Nonlinear Eigenvalue Problems

Nonlinear eigenvalue problems arise in many fields of naturaland engineering sciences. Theoretical and practical results arescattered in the literature and in most cases they have beendeveloped for a certain type of problem. In this book we considerthe most general nonlinear eigenvalue problem without assumptionson the structure or spectrum and provide basic facts. NonlinearRayleigh functionals are analyzed in detail and in different forms.New methods for the computation of eigenvalues and -vectors aredesigned based on Rayleigh functionals, and well-knownJacobi--Davidson methods are discussed. Asymptotically cubicconvergence of the two-sided nonlinear Jacobi--Davidson method isshown. The special case of nonlinear complex symmetric eigenvalueproblems is examined. We show the appropriate definition of acomplex symmetric Rayleigh functional, which is used to derive acomplex symmetric Rayleigh functional iteration which convergeslocally cubically, and the complex symmetric residual inverseiteration method. All methods are also illustrated numerically. Thebook is addressed to mathematicians as well as engineers interestedin nonlinear eigenvalue problems.

Autorentext

Kathrin Schreiber, Dipl.-Math., studied Mathematics in Dresden and Glasgow, completed her Ph.D. at Technische Universität Berlin in 2008.