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"Stability" refers to at least two distinct concepts in scientific computing:

  • inexactness of floating point arithmetic, backward error analysis, etc
  • discretization/operator stability, a necessary part of a well-posed discrete problem

The stability tag claims to be the former, but actually contains more of the latter. The tag was created after several of the defining questions in that category, and really needs to be revised. Should the floating-point tag be clarified and used to catch those currently using "stability" to mean floating point stability, with "stability" revised for discretization/operator stability? Or some other scheme?

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Both concepts of stability refer to whether small errors have a small impact on the solution. Only the source of errors differs (roundoff errors versus truncation errors). I personally think it's fine to have them both under one tag.

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