What is the Newton Raphson Method? Derive formula for it.

What is the Newton Raphson Method(NR)?

What is the Newton Raphson Method?. This method falls in the category of open bracketing methods. It is also called the method of tangents as it determines the root of an equation by drawing the tangent to the function at initial guess. This method converges very fast and it fails only when the derivative of the function at the initial guess become equal to zero.

Derivation of NR method

There are two approaches to derive the formula for this method.

  1. Using Taylor’s series 
  2. Using Graphical Interpretation

Taylor’s series use for deriving Newton Raphson Formula

Let x0 be the initial guess and the value of the function at this point is f(x0). Lets assume that x0+h be the next value or better approximation to the root of the function f(x)=0 where h is very very small. Then according to Taylor’s series expansion formula

derivation of Newton Raphson method using taylor's series
derivation of Newton Raphson method using Taylor’s series

Geometrical Interpretation of NR Method

Geometrical Interpretation of Newton Raphson Method 
Geometrical Interpretation of Newton Raphson Method
derivation of newton Raphson method
derivation of newton Raphson method

Develop an iterative formula for finding the square root of any positive integer using NR method

Develop an iterative formula for finding the square root of any positive integer using NR method

For more detail watch here 

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https://eevibes.com/mathematics/numerical-analysis/what-is-the-bisection-method/

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