I occasionally see these terms used and I'm not really sure what is meant by all of them. Is it possible for an asymptotic bound that is not Big $\\Theta$ bound to be "tight"? What does it mean for ...
The key takeaway for me is that, we can do worst-, best- case analysis on anything of the asymptotic bounded functions. To me, that shows the independence of Big O vs. worst case analysis. Thanks!
What does it mean that the bound $2n^2 = O(n^2)$ is asymptotically tight while $2n = O(n^2)$ is not? We use the o-notation to denote an upper bound that is not asymptotically tight. The definitions...
The last times i was searching a lot to understanding Big O notation or in general asymptotic notations concepts because i didnt hear about it or them before starting studying in computer science....
In short asymptotic complexity is a relatively easy to compute approximation of actual complexity of algorithms for simple basic tasks (problems in a algorithms textbook). As we build more complicated programs the performance requirements change and become more complicated and asymptotic analysis may not be as useful.
From what I have learned asymptotically tight bound means that it is bound from above and below as in theta notation. But what does asymptotically tight upper bound mean for Big-O notation?
I think that definition 2 of the dictionary you link is closer to the truth, i.e. two functions with the same asymptotic behaviour need not be numerically similar, but are similar in another sense (that is, in their asymptotic behaviour). What the lecturer actually meant is of course another thing entirely...
The asymptotic growth of $4 \log n$ is referred to as $\Theta (\log n)$. You will have to look at the definition of asymptotic growth to see why that is the case, but intuitively, it is the growth of a function when we discard constant factors and only look at the function "in the limit".
