I have a task to find a function with the best order of convergence and use it in my solution. I have come to the conclusion that both my functions have the same order of convergence and are sublinear. However, one of them is converging to 1 faster than the other. Does this mean that it is "better" in terms of cost when doing calculations?
2026-03-30 08:37:33.1774859853
Which function is better to use if both are sublinear and have the same order of convergence?
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No. Methods should be classified as good or bad depending on their reliabilty, accuracy and speed. Assuming that your methods all achieve the target accuracy for all valid input, then the deciding factor is the time spent to produce that output. This is highly implementation and machine dependent.
If at all possible try to device a method for which the convergence is at least linear.