excuse my weak math language and skill, came here to look for help :) any answer will be much appreciated and useful to me.
we have to do a research on the newton raphson method in numerical analysis, but i have no clue what the method do or even how to use it, i looked up some stuff on the internet but they weren't so useful to me(not simple enough for me to understand), cause i'm not that great at math so i came here asking for help.
what i need to do is find a problem, explain it and its solution and a bit explanation of the method itself and to explain if its well posed? and what does also well posed mean ?. and also write about the history of the method.
sorry if i'm asking too much or if i'm asking the wrong question, this place seems full of people who know stuff about math :), any answer will be appreciated and helpful to a fellow student xD, even if you direct me to places with simple information that a normal guy can understand that will be helpful as well.
thanks in advance, and hope u have a nice day :)
First thing i checked was wikipedia, http://en.wikipedia.org/wiki/Newton%27s_method, and i understood its a method to find approximations for the roots of a function. Like $f(x)=0$. If i got a normal function like $ax^2+bx+c = 0$ i think i can find the roots of the function.
- But i don't understand the concept of approximations. Do i have the function? And i cant solve it so i have to search for approximations. And do i know how many roots the function has? Is it polynomial?
Second website i checked was http://math.ubc.ca/~anstee/math104/104newtonmethod.pdf its a pdf article which made stuff easier and harder at the same time.
- Like what is a well defined function?
- And what is the first guess. ? And how do i iterate guesses ? And what is the h ( difference from real root ) !
- And what kinds of functions is it good for ? Like all kind of functions ?
- And how can i make a second guess after the first one. And how do i know if its better and closer to the real root ? Or do i just say $x_0$ and $x_1$ is that enough ? Is it theoretical ? Or does provide real numbers ?
Third place i checked was http://jstor.org/stable/2973939?seq=1#page_scan_tab_contents and its an article of the american math journal . They showed the calculation that newton did and how he noticed that its failing because of wrong guess is far from real root.
But still i didn't understand how he did the calculations and how the method is actually used . But here i was looking for the methods history and how it was developed and not how to use it.
And what is numerical solving ? Is different from algebraic solving ?