If I for example after "9" iterations get the following :
p_9 = 1.365234375
and the actual p is given as:
p = 1.365230013
Is it simply saying that p_9 is within 10^-4 because the first 4 numbers 1.365 match up?
What is "find a solution accurate to within 10^-4 mean in Bisection method?
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$\begingroup$
numerical-methods
approximation
rounding-error
bisection
2 Answers
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It likely means $$ \lvert p - p_9 \rvert < 10^{-4} $$
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0So if i am understanding this, as long as the absolute error is less than or equal to some tolerance (10^-4) in this case then it is "within" that tolerance? – 2017-02-17
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In the bisection method, you have a bracketing interval $[a_k,b_k]$ that gets bisected in every step. As the exact point and the next midpoint are both inside this interval, the condition to check is $$ |b_k-a_k|<10^{-4}, $$ as the error is guaranteed to be smaller than that.