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While searching for good initial guess to newton-raphson method for solving nonlinear algebraic system of equations, I found homotopy continuation method. However, I don't understand this: Homotopy turns the system into an easier system by changing its factor to 0 and increasing gradually till it becomes 1 every time to produce a new set of equations. 1) What I don't understand is how does it solve the first simplified system to get initial guesses? Doesn't this system also need initial guess to be solved by newton-raphson?

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