Question

Difference between bisection method , newton raphson and regula false method

Answer 1

Within numerical analysis, Newton-Raphson is simply a method for finding successively better (accurate) approximations to the zeroes which are more commonly referred to as roots of a real-valued "function." <br />
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The difference between the two is such that the Newton-Raphson method is a much more efficient method than other "simple" methods such as the bisection method. I'm going to take it so that I can assume you know that the NR method requires the calculation of the derivative of a function at the reference point, which is not always the easiest thing to do. <br />
Indeed, you'll be able to see that the tangent line often "shoots" off wildly and may occasionally be trapped in a loop. Unfortunately, the promised efficiency is then unfortunately far too simplistic to be accurate. <br />
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The NR method is only guaranteed to converge if certain conditions are satisfactory at the outset. If the assumptions made in the proof of quadratic convergence are satisfied, the method will reach static convergence. In certain cases (not all), the conditions on function necessary for such convergence are satisfactory, but the point chosen as the initial point is not actually within the interval where the method finds and achieves convergence. This is where a different method, such as the bisection method should be used so that a far better estimate for the zero is gained and applicable as an initial point.<br />
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