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 Post subject: help me fastPosted: Fri, 27 Mar 2009 08:37:14 UTC
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Joined: Fri, 27 Mar 2009 08:27:30 UTC
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i need an example in which newtons method converge with order 3
its in numerical analysis
thanx

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 Post subject: Re: help me fastPosted: Fri, 27 Mar 2009 09:28:51 UTC
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math 1 wrote:
i need an example in which newtons method converge with order 3
its in numerical analysis
thanx

Hint: something with f''(root)=0.

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 Post subject: hiPosted: Fri, 27 Mar 2009 12:44:14 UTC
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can you give more details like an example

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 Post subject: Re: hiPosted: Fri, 27 Mar 2009 12:58:49 UTC
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math 1 wrote:
can you give more details like an example

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 Post subject: hiPosted: Fri, 27 Mar 2009 13:10:15 UTC
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Posts: 110
i thought of
f(x)=the therd root of any poly.
im not that smart or even have big imagenatin to think of a function that its second derivative and its first =0 and the therd is not ill be greatfull if you could help
thanx

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 Post subject: Posted: Fri, 27 Mar 2009 14:55:38 UTC
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 Post subject: thanksPosted: Fri, 27 Mar 2009 15:04:18 UTC
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thank you i never thought it is that simple

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 Post subject: Posted: Fri, 27 Mar 2009 15:07:01 UTC
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robbwrr wrote:

... except it doesn't work for the original problem. I'll leave math 1 to figure out how to tweak it.

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 Post subject: :)Posted: Fri, 27 Mar 2009 15:11:06 UTC
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Joined: Fri, 27 Mar 2009 08:27:30 UTC
Posts: 110
ok ill think of it if it work and i found it ill tell you but if i didnt ill tell you too maby ill get some thing new

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 Post subject: hiPosted: Fri, 27 Mar 2009 15:28:06 UTC
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Joined: Fri, 27 Mar 2009 08:27:30 UTC
Posts: 110
how is this one
f(x)=(cosx-x)^3
am i right or its wrong

Last edited by math 1 on Fri, 27 Mar 2009 16:59:51 UTC, edited 2 times in total.

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 Post subject: thank youPosted: Fri, 27 Mar 2009 16:58:51 UTC
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Joined: Fri, 27 Mar 2009 08:27:30 UTC
Posts: 110
thanx to both of your help

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 Post subject: Re: hiPosted: Fri, 27 Mar 2009 17:01:06 UTC
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math 1 wrote:
how is this one
f(x)=(cosx-x)^3
am i right or its wrong

No, that won't work either. Read my first hint carefully --- there is a subtler hint there.

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 Post subject: Posted: Fri, 27 Mar 2009 17:04:27 UTC
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Joined: Fri, 27 Mar 2009 08:27:30 UTC
Posts: 110
have you tryed the second derivative on the root is zero if im not mestaken

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 Post subject: Posted: Fri, 27 Mar 2009 17:15:29 UTC
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Joined: Fri, 27 Mar 2009 08:27:30 UTC
Posts: 110
by newtons method the root of cosx-x is approximatly 0.739085......
so i think its right what about you what do you think
if it wrong then give me an example
thank you

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 Post subject: Posted: Fri, 27 Mar 2009 17:36:19 UTC
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OK, so spelling that out a bit more

Hint: I have said nothing about f'(root) --- there is a condition that you need to find out for yourself. Note what f'(root) is for robbwrr's and your suggestions.

Once you get that, the proof is just Taylor expand , where is the root and

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