Is it possible to know a problem instance is III-posed?. some foundations for a general theory of condition numbers

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Abstract

We develop some foundations for a general theory of condition numbers, ill-posed problem instances, and related concepts. Justification for our formalizations is provided by results from semi-algebraic geometry, with particular reliance on the fact that decision methods for the first-order theory of the reals exist, as was proven by Tarski. © 1994 Academic Press, Inc.

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Renegar, J. (1994). Is it possible to know a problem instance is III-posed?. some foundations for a general theory of condition numbers. Journal of Complexity, 10(1), 1–56. https://doi.org/10.1006/jcom.1994.1001

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