We present a method to solve large optimization programs with bilinear matrix inequality (BMI) constraints. Such programs arise in control applications such as system analysis, controller synthesis or filter design. Our specific point of view here is to cast BMI problems as nonconvex eigenvalue optimization programs and to use nonsmooth optimization methods suited for eigenvalue optimization to...

We investigate algorithms for solving large sparse symmetric matrix eigenvalue problems resulting from finite element discretizations of steady state electromagnetic fields in accelerating cavities. The methods have been applied to the new design of the accelerating cavity for the PSI 590 MeV ring cyclotron. The solutions of this kind of eigenvalue problems can be polluted by so-called spurious...

The simulation of drift instabilities in the plasma edge leads to cubic polynomial PDE eigenvalue problems with parameter dependent coefficients. The aim is to determine the wave number which leads to the maximum growth rate of the amplitude of the wave. This requires the solution of a large number of PDE eigenvalue problems. Since we are only interested in a smooth eigenfunction corresponding ...

In the 1960s, Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems. Many theoretical results and numerical methods for nonsingular multiparameter eigenvalue problems are based on this relation. In this paper, the above rela...

where A1, . . . , Am are given n × n matrices and the functions p1, . . . , pm are assumed to be entire. This does not only include polynomial eigenvalue problems but also eigenvalue problems arising from systems of delay differential equations. Our aim is to compute the -pseudospectral abscissa, i.e. the real part of the rightmost point in the -pseudospectrum, which is the complex set obtained...

We discuss the design and development of a new Fortran code EA16 for the computation of selected eigenvalues and eigenvectors of large-scale real symmetric eigenvalue problems. EA16 can be used for either the standard or the generalized eigenvalue problem. The underlying method used by EA16 is the block Lanczos method with partial reorthogonalization plus implicit restarting, combined with purg...

We consider solution of sparse linear systems that arise from generalized eigenvalue problems for molecular orbital calculation of the biochemistry application [2]. This application predicts the reaction and properties of proteins in water molecules through the orbital of molecules indicated by the status of electron distribution. The prediction of the electron distribution requires to obtain a...