Modified Newton's method for systems of nonlinear equations with singular Jacobian

作者：Hueso Jose L^*; Martinez Eulalia; Torregrosa Juan R

来源：Journal of Computational and Applied Mathematics, 2009, 224(1): 77-83.

DOI：10.1016/j.cam.2008.04.013

• Newton's method
• Jacobian matrix
• Order of convergence
• Fixed point function

It is well known that Newton's method for a nonlinear system has quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution. Here we present a modification of this method for nonlinear systems whose Jacobian matrix is singular. We prove, under certain conditions, that this modified Newton's method has quadratic convergence. Moreover, different numerical tests confirm the theoretical results and allow us to compare this variant with the classical Newton's method.

• 出版日期2009-2-1