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1.3. Newton - Raphson Method This is an open loop method for nding roots. One of the most widely used root-locating formulas. If the initial guess at the root is xi, a tangent can be extended from the point [xi, f(xi)]. The point where thisJangw the x-axis usually represents an improved estimate of the root. The Newton Raphson method can be derived on the basis of geometric interpretation as in the first derivative of x is equivalent to the slope: {0 ma = \" xi' xi+1 which can be arranged to yield fxi f'xi xi+1 = xi This known as the Newton - Raphson formula Algorithm for the Newton Raphson