JUCS - Journal of Universal Computer Science 1(7): 548-559, doi: 10.3217/jucs-001-07-0548
Some Algorithms Providing Rigorous Bounds for the Eigenvalues of a Matrix
expand article infoRaymond Pavec‡
‡ LIMI, Université de Bretagne Occidentale, Brest, France

Corresponding author: Raymond Pavec ( pavec@univ-brest.fr )

© Raymond Pavec.
This article is freely available under the J.UCS Open Content License.
Citation: Pavec R (1995) Some Algorithms Providing Rigorous Bounds for the Eigenvalues of a Matrix. JUCS - Journal of Universal Computer Science 1(7): 548-559. https://doi.org/10.3217/jucs-001-07-0548
Open Access
Abstract
Three algorithms providing rigourous bounds for the eigenvalues of a real matrix are presented. The first is an implementation of the bisection algorithm for a symmetric tridiagonal matrix using IEEE floating-point arithmetic. The two others use interval arithmetic with directed rounding and are deduced from the Jacobi method for a symmetric matrix and the Jacobi-like method of Eberlein for an unsymmetric matrix.