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The Behavior of the Newton-Raphson method at the singular roots has been studied by a number of authors and the convergence of the Newton-Raphson sequence has been shown to be linear. In this paper a new method with symbolic and numerical manipulations, termed the modified deflation algorithm, is proposed for the singular root of a system of nonlinear algebraic equations. The basic idea of the present method is to replace a part of the original equations by a set of new equations which passdoi:10.1016/0022-247x(87)90304-0 fatcat:pjbdidkfqfbuzfsf5cfwim3aym