Numerical Analysis Questions & Answers  
Question by Student 201427129
professor i wonder about Q#2 for Q#4-2
to solve Q#4, i must find interactions of Q#2 by secant method.
when i try, it give only condition $x_0$
accroding to lecture book, that method have 2 conditions
so i guess $x_1$ by orders of convergence to yield the at least itercations
(bisection problems are solved in #Q1 with same way
$\epsilon_{n+1}=\frac{1}{2}\epsilon_n\;\; \epsilon_k=\frac{\pi}{2^k}\;\; 3.142-\pi=\frac{\pi}{2^k} $ )

but in #Q2 problem is too hard
because it's convergence is superliner.
($k ^{p} = \frac{1} {2} *|\frac{sin(\pi)}{cos(\pi)}|=0, \epsilon =0,x_{n+1}=root) $
it means that $x_{n+1}=cost?!?!?$ so confused..
so i can't find proper and the smallest interactions
can you give some ways?
You should not determine $k$ or $p$ analytically from the function here. Rather you should find them from the error obtained at each iteration only.
Question by Student 201529190
Dear Professor, In Question #5 1,I think it should be added "|ϵ0|Newton =|ϵ0|secant ". Although does not affect the question, it will be more rigorous, and this is what you mentioned in class.
It is not necessary to distinguish between the initial error of Newton and of secant because both should be set to the same value for a fair comparison. Also, you should typeset your question better in the future and use latex for all math expressions.
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