Newton's Raphson method - for arriving at minimum using approximation

Alright the  Newton–Raphson method is used here to find the approximate value

of some variable.

looks weird right ,the idea is to try out some technique to find the 

parameter values of a function so that the loss is minimum /close to '0'

The method derives the equation as

  xn = x n-1 - f(x) /f '(x)

f(x) is some function 

f '(x) is the derivative of x  

here  i have tried some function of my own or u could see the wiki ref for example

from below u can the 1st iteration value ,but to minimse the loss we need to go for further iterations.

 

 

 

 

lets see how the 2nd iteration performs

we have arrived at the value of x at x1 so the loss which is y is zero

so what we have achieved with this u can try out some other equation 

to get the approx value , still thinking 

consider another equation x ^2 = a ,this is to find the root of a ,meaning

x = sqrt( a) .

so the idea here to to optimize some parameter now it is 'x' 

could be other parameter 'm ' or ' w1' which we use in machine learning

y =mx +b

y =w1X +b 

but newton's method has its own failure which we will see with some example 

so this should give an idea of an algorithm for optimization.

cool then bye for now - thanks.

reference -

https://en.wikipedia.org/wiki/Newton's_method