Apply newton's method to the equation $\displaystyle x^2-a=0$ to derive the following square-root algorithm: $\displaystyle Xn+1= \frac12(Xn+a/Xn)$ $\displaystyle f(x)=x^2-a$ $\displaystyle f'(x)=2x$ What's next?...
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Originally Posted by Fosite Apply newton's method to the equation $\displaystyle x^2-a=0$ to derive the following square-root algorithm: $\displaystyle Xn+1= \frac12(Xn+a/Xn)$ $\displaystyle f(x)=x^2-a$ $\displaystyle f'(x)=2x$ What's next?... Just plug into the formula for Newtons method $\displaystyle x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$ and simplify and whola you are done
Originally Posted by TheEmptySet Just plug into the formula for Newtons method $\displaystyle x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$ and simplify and whola you are done my question is which X1 should I choose? and is the final formula always contains $\displaystyle a$?
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