Numerical analysis of generalised max-plus eigenvalue problems

Numerical Analysis of Nonlinear Eigenvalue Problems

We provide a priori error estimates for variational approximations of the ground state eigenvalue and eigenvector of nonlinear elliptic eigenvalue problems of the form −div(A∇u) + V u + f(u)u = λu, ‖u‖L2 = 1. We focus in particular on the Fourier spectral approximation (for periodic problems) and on the P1 and P2 finite-element discretizations. Denoting by (uδ, λδ) a variational approximation o...

Max - Min Eigenvalue Problems , Primal -

Two Primal-dual interior point algorithms are presented for the problem of maximizing the smallest eigenvalue of a symmetric matrix over diagonal perturbations. These algorithms prove to be simple, robust, and eecient. Both algorithms are based on transforming the problem to one over the cone of positive semideenite matrices. One of the algorithms does this transformation through an intermediat...

The Numerical Treatment of Large Eigenvalue Problems

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

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