Abstract
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 pass through the singular root. According to the method, both convergency and accuracy can greatly be improved. In addition it is often possible to obtain analytically the singular root from the new equations. In order to show the effectiveness of the present method two illustrative examples are solved.
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