For mildly nonlinear systems, involving concave diagonal nonlinearities, semi-global monotone convergence of Newton’s method is guarantied provided that the Jacobian of the system is an M-matrix. However, regardless this convergence result, the efficiency of Newton’s method becomes poor for stiff nonlinearities. We propose a nonlinear preconditioning procedure inspired by the Jacobi method and resulting in a new system of equations, which can be solved by Newton’s method much more efficiently. The obtained preconditioned method is shown to exhibit semi-global convergence.
CITATION STYLE
Brenner, K. (2020). Acceleration of newton’s method using nonlinear jacobi preconditioning. In Springer Proceedings in Mathematics and Statistics (Vol. 323, pp. 395–403). Springer. https://doi.org/10.1007/978-3-030-43651-3_36
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