Abstract
In this paper, we provide bounds for the expected value of the log of the condition number C(A) of a linear feasibility problem given by a n × m matrix A (Ref. 1). We show that this expected value is O(min{n, m log n}) if n > m and is O(log n) otherwise. A similar bound applies for the log of the condition number C R(A) introduced by Renegar (Ref. 2).
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Cheung, D., Cucker, F. Probabilistic Analysis of Condition Numbers for Linear Programming. Journal of Optimization Theory and Applications 114, 55–67 (2002). https://doi.org/10.1023/A:1015460004163
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DOI: https://doi.org/10.1023/A:1015460004163