Brown-Broyden update algorithm (Q2780888)

An iteration method is proposed for numerical solution of systems of nonlinear equations \(F(x)=0\) with \(F:D\subset {\mathbb R}^n\to{\mathbb R}^n\). It is a hybrid method based on Brown's techniques which integrate the generalized LU decomposition into Newton's method, and Broyden's technique which updates the linearized coefficient matrix by columns. The proposed method preserves local superlinear convergence and structure of the two-staged interative processes in Brown's technique. Furthermore, it reduces number of calculating the function value from \(O(n^2)\) to \(O(n)\). Numerical results illustrate effectiveness of the method.