On the global convergence of Broyden's method

Considers Broyden's 1965 method for solving nonlinear equations. If the mapping is linear, then a simple modification of this method guarantees global and Q-superlinear convergence. For nonlinear mappings it is shown that the hybrid strategy for nonlinear equations due to Powell leads to R-superlinear convergence provided the search directions form a uniformly linearly independent sequence. The authors then explore this last concept and its connection with Broyden's method. Finally, the authors point out how the above results extend to Powell's symmetric version of Broyden's method

Duke Scholars

Author John A. Trangenstein Mathematics