The equation of a line with slope m passing through (x_1, y_1) would be: y - y_1 = m (x - x_1)
X_0 is the rough approximation of the root done at the first and the successive approximations go as x_1, x_2, ….į(x_n) is the function whose root is to be determined and f’(x_n) is the derivative of the function.įor a close enough approximation x_n, the better approximation of the root typically can be found by drawing the tangent to the graph at x_n and finding where the tangent intersects the x-axis. Newton’s method, also known as Newton-Raphson method is a root-finding algorithm that produces successively better approximations of the roots of a real-valued function. Why don’t you implement it in your system? Newton’s method Let’s see it in the whiteboard now with n = 4. The approximate root is the square root we want.Continue step 2 until the difference in the approximate root along the iterations is less than the desired value (or precision value).Add the approximate root with the original number divided by the approximate root and divide by 2.Take a reasonable guess (approximate root) for the square root.Probably, some of you hated too seeing his name everywhere - from math textbook to physics textbook, from classical mechanics to heat and thermodynamics, and from optics to cubics. I am bringing your old friend Newton (and Raphson too), whom you loved a lot during your school days. Yes, I am rescuing you from that situation if the day comes. But what if you are in a place where electricity is not available and your gadgets are dead? Yes, that can be done in a straight forward way.
We have built-in functions (or commands/buttons) in our calculators, computers, programming languages, mobiles and everywhere to calculate the square root. Whether it is finding the square root of a number or square root of a sum of squares, a function (or command) to find the square root of a number is needed. You can’t do these without one thing - square root. Given the dimension of a door, you need to know how big plywood can be passed through the door. Given a number of total students in a school and you want to know if all the students fit in an assembly ground, you need to know how many lines need to be formed at a minimum.
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