1. Newton's Method on TI-84

I am adding the program to calculate zero's using Newton's Method, I was wondering what the significance of 2 commands are when putting them in. the whole string is:
N+1>N:X-y1(x)/y2(x)>x:{N,X,Y1(x)}

I was wondering what these two commands actually meant in terms of application of newton's method.

1) N+1>N

2) {N,X,Y1(x)}

2. Originally Posted by ski4life912
I am adding the program to calculate zero's using Newton's Method, I was wondering what the significance of 2 commands are when putting them in. the whole string is:
N+1>N:X-y1(x)/y2(x)>x:{N,X,Y1(x)}

I was wondering what these two commands actually meant in terms of application of newton's method.

1) N+1>N

2) {N,X,Y1(x)}

If you have a differentiable function f and you want to calculate a zero of f then you need first a guess (usually called $\displaystyle x_0$) which value of x will give f(x) near zero. Then you can start an iterating process to get an approximative value of the zero by:

$\displaystyle x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$

If you take the commands and keep in mind that the sign ">" means "store":

N+1>N ..... The counter increases by 1 and is stored in the variable N

X-y1(x)/y2(x)>x ..... Calculate the next value of x and store the value in the variable X. It is necessary here that f(x) is stored in y1(x) and f'(x) in y2(x).

{N,X,Y1(x)} ..... Collect all results in a list so the output can be organized much easier.

By the way: With this program it is absolutely necessary to define a condition which ends the calculations. Otherwise your calculator will be caught in an endless loop.