Convergence of partially asynchronous block quasi-Newton methods for nonlinear systems of equations

In this paper, a partially asynchronous block Broyden method is presented for solving nonlinear systems of equations of the form F(x) = 0. Sufficient conditions that guarantee its local convergence are given. In particular, local convergence is shown when the Jacobian F′(x∗) is an H-matrix, where x∗ is the zero point of F. The results are extended to Schubertʹs method. A connection with discrete Schwarz alternating procedure is also shown.