Subsidized by the NSF of China (10726006);by the China Postdoctoral Science Foundation(20070421155);by the SRPHEXJ(XJEDU2007S07);by the Doctor Foundation of Xinjiang University
冯新龙, 帕力旦·赛力提尼亚孜, 张知难. 有理随机矩阵非奇异的概率(英文)[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2008, 110(2): 174-177.DOI：
有理随机矩阵非奇异的概率(英文)
摘要
证明了随机浮点数矩阵非奇异的概率接近于1
从而表明在求具有秩亏损的有理浮点数矩阵的秩时
没有一种数值算法是有效的.
Abstract
In this paper
we show that the probability of a random floating number matrix is nonsingular nears 1.Thus no numerical algorithm is effective for determining the rank of a random floating number matrix
which is original rank-deficient.
关键词
Keywords
references
Golub G H,Van Loan C F.Matrix Computations[M].The Johns Hopkins University Press,1993.
Golub G H,Van Loan C F.Matrix Computations[M].The Johns Hopkins University Press,1996.
Golub G H,Wilkinson J H.Conditional Eigensystems and the Computation of the Jordan Canonical Form[J].SIAM Review,1976,18: 578-619.
Wilkinson J H.The Algebraic Eigenvalue Problem[M].Oxford University press,1965.
Zhang Zhi-nan.The Jordan Canonical Form of A real Random Matrix[J].Numerical Mathematics A Journal of Chinese Universities,2001,23(4):363-367.
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