An Orthogonal High Relative Accuracy Algorithm for the Symmetric Eigenproblem, Tech. report, available online at http://www.uc3m.es/uc3m/dpto/MATEM/molera/indice.html

Abstract. We propose a new algorithm for the symmetric eigenproblem that computes eigen-values and eigenvectors with high relative accuracy for the largest class of symmetric, definite and indefinite, matrices known so far. The algorithm is divided into two stages: the first one com-putes a singular value decomposition (SVD) with high relative accuracy, and the second one obtains eigenvalues and eigenvectors from singular values and vectors. The SVD, used as a first stage, is responsible both for the wide applicability of the algorithm and for being able to use only orthogonal transformations, unlike previous algorithms in the literature. Theory, a complete error analysis, and numerical experiments are presented