We prove that the Jacobi algorithm applied implicitly on a decomposition A = XDXT of the symmetric matrix A, where D is diagonal, and X is well conditioned, computes all eigenvalues of A to highâ€¦ (More)

Componentand normwise perturbation bounds for the block LU factorization and block LDLâˆ— factorization of Hermitian matrices are presented. We also obtain, as a consequence, perturbation bounds forâ€¦ (More)

Least squares problems minx â€–bâˆ’Axâ€–2 where the matrix A âˆˆ CmÃ—n (m â‰¥ n) has some particular structure arise frequently in applications. Polynomial data fitting is a well-known instance of problems thatâ€¦ (More)

We present a Weyl-type relative bound for eigenvalues of Hermitian perturbations A + E of (not necessarily definite) Hermitian matrices A. This bound, given in function of the quantity Î· =â€¦ (More)

A singular matrix A may have more than one LU factorizations. In this work the set of all LU factorizations of A is explicitly described when the lower triangular matrix L is nonsingular. To thisâ€¦ (More)

We propose a new algorithm for the symmetric eigenproblem that computes eigenvalues and eigenvectors with high relative accuracy for the largest class of symmetric, definite and indefinite, matricesâ€¦ (More)

In this talk we will review the basic facts and results in the field of high relative accuracy. We will see which algorithms and for which classes of matrices give high relative accuracy. Inâ€¦ (More)