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This book provides an analysis of the boundary element method for the
numerical solution of Laplacian eigenvalue problems. The representation
of Laplacian eigenvalue problems in the form of boundary integral
equations leads to nonlinear eigenvalue problems for related boundary
integral operators. The concept of holomorphic Fredholm operator
functions is used for the analysis of the boundary integral formulations
of Laplacian eigenvalue problems. A convergence and error analysis for
the Galerkin approximation of eigenvalue problems for holomorphic
coercive operator functions is established. These results are applied to
the Galerkin boundary element discretization of Laplacian eigenvalue
problems. Different methods for the solution of algebraic nonlinear
eigenvalue problems such as inverse iteration, Rayleigh functional
iterations and Kummer‘s method are presented. For the latter method a
numerical analysis for simple and multiple eigenvalues is given. In a
numerical example, a boundary element and a finite element approximation
of a Laplacian eigenvalue problem are compared. The theoretical results
of the analysis of the boundary element method could be confirmed.