On the Convergence of the Factorization Update Algorithm

In this paper, we make a Kantorovich-type analysis for the spares Johnson and Austria's algorithm given in 2], which is called factorization update algorithm. When the mapping is linear, it is shown that a modification of that algorithm leads to global and Q-superlinear convergence. Finally, we point out the modification is also of local and Q-superlinear convergence for nonlinear systems of equations and give its corresponding Kantorovich-type convergence result.