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Newton-Raphson Method: This is a fixed-point estimation method.
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Newton Raphson Newton-Raphson Method: This is a fixed-point estimation method. The estimate starts at x 1,for a root of f(x) = 0. A tangent is then draw to the curve y = f(x) at the point (x 1, f(x 1)). The point at which the tangent cuts the x-axis then gives the next approximation for the root, and the process is repeated. I am going to use the equation y = x³ - 3x + 1. *** As you can see there are three roots in this graph, they are in the interval [-2, -1] [0, 1] [1, 2] The gradient for the tangent to the curve at (x 1, f(x 1)) is f'(x 1) (meaning dy/ dx for x). The equation of the tangent is: y-y1 = m(x-x1). Therefore y-f(x1) = f'(x1) [x-x1]. This tangent passes through the point (x2, 0). Carrying on with this process, this will get closer and closer to the tangent. But...
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