User:Pooja929

My User Page

List of five things I have learnt about Wikipedia/Wikiversity are:

Wikipedia is an online encyclopedia that is available for free. It provides information on every possible subject and also allows users to edit pages or articles that have been posted.
Wikipedia also supports display of content in multiple languages.So this is a very good approach to reach out to every person all over the world by making it multi linguistic.
Wikimedia Foundation is the host that has started out this project called Wikipedia. Along with this there are 9 other projects under its umbrella. One that is scoped for my interest is Wikiversity along with Wikipedia.
Wikiversity is a portal where people from different universities like students, lecturers and research scientists can update their latest findings or share their knowledge to the world.As well known this site helps in collaborative learning. It is like an open discussion forum for people to put forward their findings or any study material that could help others and allow others to share their views regarding the same.
Now I have learnt how to edit my page in Wikipedia using link Editing Tutorial

Some complicated Math Formula

1) The cubic formula:
The solution for $ax^{3}+bx^{2}+cx+d=0$
$x={\sqrt[{3}]{({\frac {-b^{3}}{27a^{3}}}+{\frac {bc}{6a^{2}}}-{\frac {d}{2a}})+{\sqrt {({\frac {-b^{3}}{27a^{3}}}+{\frac {bc}{6a^{2}}}-{\frac {d}{2a}})^{2}+({\frac {c}{3a}}-{\frac {b^{2}}{9a^{2}}})^{3}}}}}+{\sqrt[{3}]{({\frac {-b^{3}}{27a^{3}}}+{\frac {bc}{6a^{2}}}-{\frac {d}{2a}})-{\sqrt {({\frac {-b^{3}}{27a^{3}}}+{\frac {bc}{6a^{2}}}-{\frac {d}{2a}})^{2}+({\frac {c}{3a}}-{\frac {b^{2}}{9a^{2}}})^{3}}}}}-{\frac {b}{3a}}$

Source for formula [1]

Modification to Fixed point Iteration Wikipedia Page

The current "Fixed Point Iteration" wikipedia page is good but misses out some detailed analysis about the iteration method. After browsing through lot of content from other internet resources I feel the content given below could be appended to the current page. This appending may help to enhance the information about the iteration method.
Fixed point iteration is given as : $x_{n+1}=f(x_{n}),\,n=0,1,2,\dots$

Methodological error found with this iteration is missing from the page. I strongly feel this could be a good one to be added.

Methodological Error
The link to the sourse of this claim has been collected from [2]
The error of the fixed point iteration method can be shown as:
$E_{n+1}=|g'(y)|E_{n}$

Where y is some point between $x_{n}$ and the fixed point
The condition that $|g'(y)|<1$ can be difficult to show and it can also be very difficult to automate the value.
But now let us tune the equation given above in such a way that we are plugging the exact value of root say r into it.So let us modify it to $E_{n+1}=|g'(r)|E_{n}$
The above error equation shows us that

the error reduces if $|g'(r)|<1$ , the scheme converges,
the error increases if $|g'(r)|>1$ , the scheme diverges.

When the scheme converges we can see that

the error will decrease monotonically if 0 ≤ g'(r) < 1,
the error decreases in an oscillatory manner if -1 < g'(r) < 0.

A much more useful technique is to check if the difference of successive approximations is converging.
Thus we check the value $|a_{n+1}-a_{n}|$ on each iteration.
If the value $|a_{3}-a_{2}|>|a_{2}-a_{1}|$ we should abort the iteration.

Project Proposal

Adding more of quizzes to Numerical Analysis's wikiversity page would be exciting. It involves coding though in a small way but is more fun. Quiz will cover questions from all the topics that we have covered so far as part of our syllabus. The questions would be taken from few Numerical Analysis text books. Quiz would go according to levels.First the person gets to choose the topic of his choice and take up a quiz. Then in that topic after answering few of the basic questions he could move onto the next level of questions which would be tough. So the quiz is designed in the form of levels.This design would help students learn in stages.