This note presents a new piecewise linear homotopy continuation method for solving a system of nonlinear equations. The important feature of the method is the use of an odd map for the artificial level of the homotopy. Some sufficient conditions for the global convergence of the method are given. They are different from the known conditions for the global convergence of the existing homotopy continuation methods. Specifically, they cover all the systems of nondegenerate linear equations.
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