Relatively robust representations of symmetric tridiagonals
The triangular factorization of an unreduced symmetric tridiagonal matrix is considered with respect to relative changes in the nontrivial entries of the lower left matrix and the diagonal part. The effect of these changes is modeled by diagonal scaling matrices. Relative changes in the eigenvalues of the tridiagonal matrix are studied in detail with respect to the inner perturbations induced by the scaling matrix. Furthermore, an algorithm for computing numerically orthogonal eigenvectors is sketched. This algorithm does not rely on the Gram-Schmidt process but requires conditions on the locus of eigenvalues.
scientific article; zbMATH DE number 1443447