Some Algorithms Providing Rigorous Bounds for the Eigenvalues of a Matrix

Raymond Pavec (LIMI, Université de Bretagne Occidentale, France)

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.