The Numerical Solution of Eigenvalue Problems

Numerical Solution of Linear Eigenvalue Problems

We review numerical methods for computing eigenvalues of matrices. We start by considering the computation of the dominant eigenpair of a general dense matrix using the power method, and then generalize to orthogonal iterations and the QR iteration with shifts. We also consider divide-and-conquer algorithms for tridiagonal matrices. The second part of this survey involves the computation of eig...

Numerical Solution of Large Nonsymmetric Eigenvalue Problems

Numerical Solution of Eigenvalue Problems with Spectral Transformations

Title of dissertation: NUMERICAL SOLUTION OF EIGENVALUE PROBLEMS WITH SPECTRAL TRANSFORMATIONS Fei Xue, Doctor of Philosophy, 2009 Dissertation directed by: Professor Howard C. Elman Department of Computer Science Institute for Advanced Computer Studies This thesis is concerned with inexact eigenvalue algorithms for solving large and sparse algebraic eigenvalue problems with spectral transforma...

Numerical Solution of Quadratic Eigenvalue Problems with Structure-Preserving Methods

Numerical methods for the solution of large scale structured quadratic eigenvalue problems are discussed. We describe a new extraction procedure for the computation of eigenvectors and invariant subspaces of skew-Hamiltonian/Hamiltonian pencils using the recently proposed skew-Hamiltonian isotropic implicitly restarted Arnoldi method (SHIRA). As an application we discuss damped gyroscopic syste...

The Numerical Treatment of Large Eigenvalue Problems

This paper surveys techniques for calculating eigenvalues and eigenvectors of very large matrices.