# The algebraic eigenvalue problem

@inproceedings{Wilkinson1965TheAE, title={The algebraic eigenvalue problem}, author={James Hardy Wilkinson}, year={1965} }

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.

## 7,694 Citations

### Deferred correction for the integral equation eigenvalue problem

- MathematicsThe 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

- Mathematics
- 1996

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

- Mathematics
- 1982

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

- Mathematics
- 1997

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

- MathematicsSIAM Rev.
- 2001

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

- Mathematics
- 1986

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

- MathematicsSIAM J. Matrix Anal. Appl.
- 2000

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.