Factorization of diagonally dominant operators on $l^{1}$

Doubly Diagonally Dominant Matrices

We consider the class of doubly diagonally dominant matrices (A = [ ajj] E C”, ‘, la,,1 l”jjl > Ck+ i laiklCk+ jlajkl. i #j) and its subclasses. We give necessary and sufficient conditions in terms of the directed graph for an irreducibly doubly diagonally dominant matrix to be a singular matrix or to be an H-matrix. As in the case of diagonal dominance, we show that the Schur complements of do...

A note on nonnegative diagonally dominant matrices

A New Perturbation Bound for the LDU Factorization of Diagonally Dominant Matrices

This work introduces a new perturbation bound for the L factor of the LDU factorization of (row) diagonally dominant matrices computed via the column diagonal dominance pivoting strategy. This strategy yields L and U factors which are always well-conditioned and, so, the LDU factorization is guaranteed to be a rank-revealing decomposition. The new bound together with those for the D and U facto...

Perturbation theory for the LDU factorization and accurate computations for diagonally dominant matrices

We present a structured perturbation theory for the LDU factorization of (row) diagonally dominant matrices and we use this theory to prove that a recent algorithm of Ye (Math Comp 77(264):2195–2230, 2008) computes the L , D andU factors of these matrices with relative errors less than 14n3u, where u is the unit roundoff and n × n is the size of the matrix. The relative errors for D are compone...

Factorization of Operators on C

Let A be a C∗-algebra. We prove that every absolutely summing operator from A into l2 factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite dimensional examples that show that one can not replace the 4-Schatten-von Neumann class by p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of cap...