Newton%27s algorithm in python
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Newton's method (also known as the Newton-Raphson method or the Newton-Fourier method) is an efficient algorithm for finding approximations to the zeros (or roots) of a real-valued function f(x). The iteration goes on in this way:
At first we deduce the general integration formula based on Newton’s forward interpolation formula and after that we will use it to formulate Trapezoidal Rule and Simpson’s 1/3 rd rule. The Newton’s forward interpolation formula for the equi-spaced points x i , i =0, 1, …, n, x i = x 0 + ih is