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- by ♪⚝Sanjiv❀Jaiswal❁⩸ 7 months ago

↪ The Newton-Raphson’s Method or Newton’s Method is a powerful technique for solving

equations numerically.

↪ Let f(x) be a well-behaved function and let x be a root of the equation f(x) = 0. We start

with an estimate x_{0} of x. From x_{0}, we produce an improved estimate x_{1}. From x_{1} we

produced a new estimate x_{2}. From x_{2}, we produce a new estimate x_{3}. We go on until we

are close enough to r or until it becomes clear that we are getting nowhere. The above

general style of proceeding is called iterative. Of the many iterative root finding

procedures, the Newton Raphson’s Method, with its combination of simplicity and power,

is most widely used.

⁕ NEWTON RAPHSON’S ITERATION

↪ Let f(x) = 0 be an equation and x be its root. Let x_{0} be a good estimate of x then for a

point (x, y) sufficiently close to it the function can be approximated by its tangent line.

↪ This tangent line crosses the x-axis when y = 0. Denote this new value of x by x1

↪ This x intercept gives a better approximation to the function's root than the original

guess.

↪ Continue in this way, if xn is the current estimate, then the next estimate x_{n} + 1

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