1. ## 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 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.

2. ## Re: newton-raphson formula

I guess your equation is $f(x)=2xln(x)-1$ right?

then, just use the definition,

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

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

substitute and simplify

3. ## 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.

4. ## Re: newton-raphson formula

thank you chaps.i will give it a go : )