Question

I am struggling on ps2 with Newton's method. I really just need to understand the concept of how it works. I have little to no understanding of calculus. If you could point me to a source that would help i'd appreciate it.

Got the first two parts correct (derivatives and polynomials)

Answer 1

ps2?

Answer 2

problem set 2 of course 6.00ocw

Answer 3

So using Newton's method in general, or for a certain function?

Answer 4

here is the pdf
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-00sc-introduction-to-computer-science-and-programming-spring-2011/unit-1/lecture-6-recursion/MIT6_00SCS11_ps2.pdf

Answer 5

it's down a little bit. The third part to the problem.
I just do not know where to start.

what variables to use. Where I should loop, if i should loop

Answer 6

So you are able to compute the derivative and evaluate a polynomial?

Answer 7

Yes

Answer 8

Okay, we start out with \(x_n=x_0\). We want to do \(x_{n+1} = x_n - f(x_n)/f'(x_n)\).

Answer 9

How would you calculate \(f(x_n)\) in your code?

Answer 10

so xn would be the root that we are trying to find?

Answer 11

What \(x_n\) is some number which is close to our root, and \(x_{n+1}\) is supposed to be a bit closer.

Answer 12

Regardless, do you understand how to implement this programmatically?

Answer 13

You should realize that \(f(x_n)\) → `evaluate_poly(poly, x_n)`

Answer 14

these are the arguments allowed:
def compute_root(poly, x_0, epsilon):

So x_0 is a random guess, that we make up. epsilon is the accuracy and poly is the polynomial.

Would I be using the derivatives from the code I have already done

Answer 15

Okay I see what your saying

Answer 16

You can calculate the derivative just once and save it. `dpoly = compute_derivative(poly)`

Answer 17

yes

Answer 18

You can let \(x_n=x_0\) at the beginning.

Answer 19

Ok it's clicked with me now. Thanks for your help. I will be right from here :)