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When doing computation, there are different types of solutions: analytical, closed form, iterative, algorithmic, exact, approximate, ... (there are probably more than I just listed and please don't hesitate to add more)

  1. I was wondering what these types mean?
  2. Are analytical and closed form solutions the same thing?
  3. Are analytical solutions and closed form solutions necessarily exact?
  4. What is the opposite to these types: analytical, closed form, iterative, algorithmic, ...? For example, is algorithmic solution the opposite of analytical solution? Is iterative solution the opposite of closed form solution?

Thanks and regards!

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"Closed form" is the term more in vogue than "analytical", I've seen. They may be exact, but a.) you'd probably need to approximate them anyway (e.g. square roots and logarithms) and b.) they may not be practical to use (see e.g. this). An "iterative" solution may very well be "algorithmic"... –  J. M. Sep 13 '11 at 23:40
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