In this paper, strong relative perturbation bounds are developed for a number of linear
algebra problems involving diagonally dominant matrices. The key point is to parameterize …

Component-and normwise perturbation bounds for the block LU factorization and block LDL
^* factorization of Hermitian matrices are presented. We also obtain, as a consequence …

In this paper, we settle Higham's conjecture for the LU factorization of diagonally dominant
tridiagonal matrices. We establish a strong componentwise perturbation bound for the …

By a block representation of LU factorization for a general matrix introduced by Amodio and
Mazzia [P. Amodio, F. Mazzia, A new approach to the backward error analysis in the LU …

In 1954, Alston S. Householder published\textit {Principles of Numerical Analysis}, one of the
first modern treatments on matrix decomposition that favored a (block) LU decomposition-the …

Antecedentes. La teoría de polinomios ortogonales respecto a medidas cuyo soporte se
encuentra en la recta real tiene un amplio espectro de aplicaciones, tales como integración …

We present the perturbation and backward error analyses of the partitioned LU factorization
for block tridiagonal matrices. In addition, we consider the bounds of perturbations for the …

The perturbation and backward error analyses of the partitioned LU factorization for block
tridiagonal matrices are presented. Moreover, we consider the perturbation bounds for the …

[16] P.-A. Absil, R. Mahony, and B. Andrews. Convergence of the iterates of descent
methods for analytic cost functions. SIAM J. Optim., 16 (2): 531–547, 2005.[17] A. Abu-Omar …

In this article, we consider the structured condition numbers for LDU, factorization by using
the modified matrix-vector approach and the differential calculus, which can be represented …