f(x) = x^2 - n.
x_{n+1} = x_{n} - f(x_{n}) / f ' (x_{n}).
See the following graph for intuition.
Note that the slope of the tangent line is f ' (x_{n}) = f(x_{n}) / {x_{n+1} - x_{n}}.
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Friday, April 9, 2010
Newton Ralphson's method to calculate square root
x^2 = n, need to find x.
f(x) = x^2 - n.
x_{n+1} = x_{n} - f(x_{n}) / f ' (x_{n}).
See the following graph for intuition.
Note that the slope of the tangent line is f ' (x_{n}) = f(x_{n}) / {x_{n+1} - x_{n}}.
f(x) = x^2 - n.
x_{n+1} = x_{n} - f(x_{n}) / f ' (x_{n}).
See the following graph for intuition.
Note that the slope of the tangent line is f ' (x_{n}) = f(x_{n}) / {x_{n+1} - x_{n}}.
Labels:
Algorithm,
numerical computation
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