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I have two iteration methods say ite1 and ite2 . If ite1 is performing well in terms of number of iterations and accuracy while ite2 is slightly better than ite1 in terms of computing time only. Which method would be better one? Could anybody clear my doubt? I would be very much thankful.

Edit 1: I want to compare my proposed iteration method with some other iteration methods. I have taken three parameters: Number of iterations, computing time, accuracy. I found that my proposed methhod has better accuracy and taking less number of iterations in comparison to other methods, while one particular method is slightly better than mine in terms of computing time only. I am confused how can i say that my method is better than others or shall I remove computing time parameter?

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I don't understand the question. You say "ite1 is better by this metric, ite2 is better by this metric, which one is better?" and then don't specify what the third use of the word "better" means. – Qiaochu Yuan Sep 23 '12 at 8:21
@QiaochuYuan I have edited my question. Does it help? – srijan Sep 23 '12 at 8:24
@srijan: your edit haven't addressed the problem. You specify particular way in which ite1 is better. Then you specify a particular way in which ite2 is better. But when you ask "which is better?" you don't specify what measure you want to compare them by. – Hurkyl Sep 23 '12 at 8:36
@Hurkyl Please take a look . I have edited again. I am extremely sorry for inconvenience. – srijan Sep 23 '12 at 8:55
Jori's answer is right. To paraphrase Hurkyl's comment on another thread, there's always an easy way to reduce the number of iterations: each iteration, you do two steps of some other algorithm. :) In the end, what matters is the total compute time it takes to achieve a given accuracy. – Rahul Mar 11 '13 at 9:03

Number of iterations is not only affecting thing. How much work each round needs? See for example

In general "best" in computer programs is not that easy to define. There might even be some very bad cases for algorithm, and then they might be very unusual (or very usual!) in reality.

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Here ite1 is better.
Because according to the Newton-Raphson iterative principal as the no of iteration is lesser(irrespective of the computing time) is presumed as the most efficient rather than such a method which involves more steps with lesser computing time.

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