Statistics How To

Well Posedness: Simple Definition for Well-Posed

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The well posedness of a problem refers to whether or not the problem is stable, as determined by whether it meets the three Hadamard criteria, which tests whether or not the problem has:

  1. A solution: s exists for all d (for every d relevant to the problem).
  2. A unique solution: s is unique for all d; for every data point d there is at most one value of s.
  3. A stable solution: s depends continously on d (a tiny change in d will lead to a tiny change in s; and a large change in d will lead to a proportionally larger change in s).

The Hadamard criteria tells us how well a problem lends itself to mathematical analysis.

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