Modified Newton’s method for systems of nonlinear equations with singular Jacobian. (English) Zbl 1159.65050

Authors’ summary: 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.


65H10 Numerical computation of solutions to systems of equations
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