The algebraic eigenvalue problem

  title={The algebraic eigenvalue problem},
  author={James Hardy Wilkinson},
Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography Index. 

Deferred correction for the integral equation eigenvalue problem

  • K. ChuA. Spence
  • Mathematics
    The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
  • 1981
Abstract This paper considers the improvement of approximate eigenvalues and eigenfunctions of integral equations using the method of deferred correction. A convergence theorem is proved and a

Accurate computation of singular values and eigenvalues of symmetric matrices

We give the review of recent results in relative perturbation theory for eigenvalue and singular value problems and highly accurate algorithms which compute eigenvalues and singular values to the

Ordinary differential equations and the symmetric eigenvalue problem

In this paper the authors develop a general framework for calculating the eigenvalues of a symmetric matrix using ordinary differential equations. New algorithms are suggested and old algorithms,

Jacobi algorithm for symmetric eigenvalue problem and integrable gradient system of Lax form

An intimate connection between matrix eigenvalue algorithms and integrable dynamical systems is studied. It is proved that an infinitesimal rotation of each step of the Jacobi algorithm for symmetric

The Quadratic Eigenvalue Problem

We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the

The geometry of matrix eigenvalue methods

This paper explores the relations between the matrix Riccati equation and the standard matrix eigenvalue methods. It is demonstrated that the mathematics of the analysis of the two objects is

On the Perturbation Theory for Unitary Eigenvalue Problems

Some aspects of the perturbation theory for eigenvalues of unitary matrices are considered and an inclusion theorem analogous to the Kahan theorem for Hermitian matrices is presented.