Summary.
Let A be an n×m real matrix and consider the linear conic system
In [Cheung and Cucker 2001] a condition number 𝒞(A) for this system is defined. In this paper we let the coefficients of A be independent identically distributed random variables with standard Gaussian distribution and we estimate the moments of the random variable ln𝒞(A). In particular, when n is sufficiently larger than m we obtain for its expected value E(ln𝒞(A))=max{ln m, ln ln n}+𝒪(1). Bounds for the expected value of the condition number introduced by Renegar [1994b, 1995a, 1995b] follow.
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Received June 12, 2001 / Revised version received October 29, 2001 / Published online November 27, 2002
RID="⋆"
ID="⋆" Partially supported by CERG grant City U 1085/02p.
Mathematics Subject Classification (1991): 65F35, 65K05
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Cucker, F., Wschebor, M. On the Expected Condition Number of Linear Programming Problems. Numer. Math. 94, 419–478 (2003). https://doi.org/10.1007/s00211-002-0385-1
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DOI: https://doi.org/10.1007/s00211-002-0385-1