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31.
We present the analysis of an interior-point method to decide feasibility problems of second-order conic systems. A main feature of this algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of arithmetic operations and the finest precision required are exhibited. 相似文献
32.
In this paper we define a new condition number ?(A) for the following problem: given a m by n matrix A, find x∈ℝ
n
, s.t. Ax<0. We characterize this condition number in terms of distance to ill-posedness and we compare it with existing condition
numbers for the same problem.
Received: November 5, 1999 / Accepted: November 2000?Published online September 17, 2001 相似文献
33.
Abstract. No abstract. 相似文献
34.
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.
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 相似文献