Help me solve this equation

[Zdravko]

I have to solve the equation

x = 0.5cosx


using the Newton method with x0 = Pi/2 and preciseness 1e-2.
For comparison with the Newton approximation I need the correct answer.

[ace007]

Using Newton's Method all the way to precision to the 15th digit is x = 0.450183611294874. In 1e-2 precision, it would be x = 0.45. Hope it helps

[Zdravko]

I said that I want the exact solution to compare with Newton method.
Anyway.
I am having difficulties applying the Newton method here. The successive approximation leads me to:

x(k+1) = x(k) + cot(x(k))


A starting value of x(0) ::= Pi/2 yields always Pi/2, or?

[akniss]

I said that I want the exact solution to compare with Newton method.


I'm curious as to what makes you think you are entitled to demand an answer to a homework question...

[Zdravko]

akniss (http://ubuntuforums.org/member.php?u=47512), I am curious why are you trolling this thread?
This is not a homework. It is a preparation for an exam.

[Zdravko]

Anyone?

[Zdravko]

Ah, I got it! The true equation is f(x) ::= x - 0.5cosx

[luisfcup]

I am also curious why you think you can demand anything, specially an exact solution for a transcendent equation!!!

I am also curious what kind of preparation are you having for an exam if you don't know that you cannot get an exact solution for any transcendent equation.

ace007 answer was the best one you could get by the way…

[Zdravko]

luisfcup (http://ubuntuforums.org/member.php?u=437027), if you haven't noticed already, this forum is created with this purpose in mind - people demand and get answers.
Yes, that's right - this is a transcendent equation.
The subject I study is called "Numerical methods". We took several approximation and interpolation methods. The exam was today. I finished it a few hours ago. I am 99% sure I solved everything in a correct way and I hope I will get a nice note.

[luisfcup]

It is called numerical methods because you don't have an analytical method to solve the problems therefor you don't have exact solutions.
The forum is for people to ask questions, not to demand answers and ace007 gave you a very nice answer.
Anyway, congratulation on your exam.

[Zdravko]

luisfcup (http://ubuntuforums.org/member.php?u=437027), no way - I have always thought this forum is for demanding things... Hmm, I must have mistaken ;)

[Blutack]

You took an exam and are on ubuntu forums 2 hours later? Surely you should either be learning the last semesters worth of stuff for the next exam or too drunk to remember your password...

[mellowd]

demand? no, you ask and if someone wants to they will answer you. It's then also curtious to say thank you.

[Zdravko]

Blutack (http://ubuntuforums.org/member.php?u=78882), yepp. What's wrong with that?