# newton-raphson formula

• Mar 30th 2012, 04:58 PM
bignaughtydog
newton-raphson formula
show that for the function f(x)=2xln*x-1, the newton-raphson formula can be expressed as

X(n+1)= (X(n)+1/2)/(1+ln*X(n)) , The (n) and (n+1) terms are subscript.

I have tried using the product rule for f(x) and then some algebraic jiggery (Headbang)but cant even get close to the raphson result.I think I may have made an error in the algebra somewhere.

Can anyone please give any suggestions???

Thank you.
• Mar 30th 2012, 10:11 PM
Re: newton-raphson formula
I guess your equation is $\displaystyle f(x)=2xln(x)-1$ right?

then, just use the definition,

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

$\displaystyle f'(x)=2+2ln(x)$

substitute and simplify
• Mar 31st 2012, 12:46 AM
froodles01
Re: newton-raphson formula
Yes, using the formula x(n+1) = x(n) - f(x) /f'(x) is the way to go
f(x) = 2x(n) ln(x(n)) - 1
f'(x) = 2(ln(x(n)+1)

substitute these into the formula, multiply terms out & cancel those terms at the top that you can (should be the 2x(n) ln(x(n)) ones)

At least that's how I did it.
• Mar 31st 2012, 03:17 AM
bignaughtydog
Re: newton-raphson formula
thank you chaps.i will give it a go : )