A modied trapezoidal Broyden's method for nonlineare quations

A modified Trapezoidal Broyden's method for nonlinear equations is presented. We design and implement an alternative approximation to Jacobian matrix of Trapezoidal Broyden’s method. This method improve the efficiency by reducing the number of iterations required by the Broyden’s method, and solve the problem that the approximate matrix almost singular or singular at some points. The local convergence properties of the new method is presented. Numerical results illustrate that the proposedmethod is efficient and robust.