Research Communication | Open Access
Volume 2021 | Communication ID 108
Volume 2021 | Communication ID 108
| A dynamical Broyden rank reduction method to solve systems of nonlinear equations |
Mostafa Ouarit, Ali Souissi, Mohammed Ziani
Received |
Accepted |
Published |
January 28, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: We propose a modification of limited memory Broyden methods, called dynamical Broyden rank reduction method, to solve high dimensional systems of nonlinear equations. Based on a thresholding process of singular values, the proposed method determines a priori the rank of the reduced update matrix. A significant reduction in the number of singular values decomposition calls of the update matrix during the iterations is observed. Local superlinear convergence of the method is proved and some numerical examples confirming the theoretical expectations are presented.