The purpose of this semester project is to investigate the Spectral Bundle Method, which is a specialized subgradient method particularly suited for solving large scale semidefinite programs that can be cast as eigenvalue optimization problems of the form min y∈R aλmax(C − m ∑ i=1 Aiyi) + b T y, where C and Ai are given real symmetric matrices, b ∈ R allows to specify a linear cost term, and a ...

A comprehensive survey of some recent results regarding parameterized inverse eigenvalue problems is given in this paper. Speciic topics include: additive and multiplicative inverse eigenvalue problems, classical inverse eigenvalue problems and generalized inverse eigenvalue problems. Both the theoretic and algorithmic aspects are reviewed. Some open problems are revealed to stimulate further r...

The rational eigenvalue problem is an emerging class of nonlinear eigenvalue problems arising from a variety of physical applications. In this paper, we propose a linearization-based method to solve the rational eigenvalue problem. The proposed method converts the rational eigenvalue problem into a well-studied linear eigenvalue problem, and meanwhile, exploits and preserves the structure and p...

Eigenvalue analysis plays an important role in understanding physical phenomena. However, if one deals with strongly nonnormal matrices or operators, the eigen-values alone may not tell the full story. A popular tool which can be useful to get more insight in the reliability or sensitivity of eigenvalues is "-pseudospectra. Apart from "-pseudospectra we consider other tools which might help to ...

This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and ...

We present a methodology for the efficient numerical solution of eigenvalue problems of full three-dimensional elasticity for thin elastic structures, such as shells, plates and rods of arbitrary geometry, discretized by the finite element method. Such problems are solved by iterative methods, which, however, are known to suffer from slow convergence or even convergence failure, when the thickn...

We present a new numerical method for computing selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. The method does not require good initial approximations and is able to tackle large problems that are too expensive for methods that compute all eigenvalues. The new method uses a two-sided approach and is a generalization of the Jacobi– Davidson type method for right d...