Newton's method(a method to find one root of any differentiable function)

 Note: If you are a beginner in programming then this will help you

Today we are going to discuss NEWTON'S METHOD ,if you know basic programming (c,c++,python or java class 11th level according to cbse) then you are definitely going to like this and if not just to stick to it.

It is method based on simple observation obviously by sir Issac Newton,to understand his observation just skip to next line.

Take any function let say f(x) and think of its graph on coordinate axis this function should be differentiable on all points on coordinates axis so initially for simplicity just think of a simple graph(like f(x)=(x^3-1).


Now take any point on x axis (let say x1) and corresponding value of y(i.e f(x1)).

Now draw tangent at (x1,f(x1)),and note the point on x axis which is common to tangent let the value be x2.

Now you have new point i.e (x2,f(x2)) on the chosen function.

Now again draw tangent on this point and note the common point on new tangent and x axis let say x3 and repeat this process some more times.

When you will repeat this you will find that value of x are heading to the root of the function.

If you want to have the general formula it is

Xn+1=Xn-(f(Xn)/f'(Xn))
where x is values on x axis and f(x) is a function and f'(x) is first differentiation of that function.

if you know basic of programming than its program on c++ will look like this


If you want to see the derivation of the general formula just see next image
There are some drawbacks also 

1)If you want to reach the correct value of root you have to choose correct value x1 and number of steps but a good programmer can solve this problem.

2)There is a problem when f'(x)=0,but again a good programmer can solve it.





Comments

Post a Comment

Popular posts from this blog

Positive thinking ....let's give a thought

Let's give a thought to POSITIVE THINKING  Doing my English assignment and they are asking to justify the statement 'positive thinking increases your work efficiency' so here are my thoughts but wait who am i to present my views ? so no one, so if you want you can just leave but may be something will hit you or may be not, so i think you are just going to give a shot so lets start, may be this is positive thinking , just joking. To represent my concept clearly about this particular topic i'am dividing any person's perspective of seeing things in three different parts either he or she has the habit of seeing things positively or the person always find something negative in any thing or he or she is of mixed type, just like the grey areas but wait i don't think grey areas exists here. So i am going to try to explain that how grey areas does not exist in this situation before this i am assuming that i am talking to a girl because i want an alternative fo...
Read more

Questioning the simple one

Image
Questioning the simple one ( something which is always in front of eyes but still looks special) Let's give our first thoughts after seeing this picture REQUEST:AFTER SEEING THESE PICTURES PLEASE MAKE SOME GUSSES, WHAT THE PICTURE IS OF THAN PROCEED 1)Atom(most childish one). 2)Amplifier 3)Camera 4)Wash basin 5)Some bacteria 6) Something under microscope 7)............. 8)...................... Let's disclose it it is just a picture of milton thermosteel bottle taken by opening its cap from top view. Those two spots are actually flash lights. If this picture is taken without flash lights it will look like this(without water also): This is how pictures are taken(through phones): So now what we are going to do  We will try to explain pictures which are looking really fascinating,so let's start. Before let's see the pictures::: A) 1)I don't know why flash light is shape of a crescent moon,in three differeent parts. ...
Read more