The aim of the book is to provide 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 solution of boundary element discretizations of such eigenvalue problems require...

Optical eigenvalue communication is a promising technique for overcoming the Kerr nonlinear limit in optical systems. The associated with Schrödinger equation remains invariant during fiber-based dispersive transmission. However, practical applications involving use of such systems are limited by occurrence fiber loss and amplified noise that induce distortion. Thus, several time-domain neural-...

We consider a matrix pencil whose coefficients depend on a positive parameter ǫ, and have asymptotic equivalents of the form aǫ when ǫ goes to zero, where the leading coefficient a is complex, and the leading exponent A is real. We show that the asymptotic equivalent of every eigenvalue of the pencil can be determined generically from the asymptotic equivalents of the coefficients of the pencil...

Three versions of an algorithm for balancing three matrices simultaneously are proposed. The balancing is performed by premultiplication and postmultiplication with positive definite diagonal matrices, in order to reduce the magnitude range of all elements in the involved matrices. Some numerically stable algorithms, when applied to matrices with a wide range in the magnitude of elements, can p...

‎Based on an eigenvalue analysis‎, ‎a new proof for the sufficient‎ ‎descent property of the modified Polak-Ribière-Polyak conjugate‎ ‎gradient method proposed by Yu et al‎. ‎is presented‎.