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• W2007175576 abstract "Numerous problems in numerical analysis, including matrix inversion, eigen-value calculations, and polynomial zero finding, share the following property: the difficulty of solving a given problem is large when the distance from that problem to the nearest “ill-posed” one is small. For example, the closer a matrix is to the set of noninvertible matrices, the larger its condition number with respect to inversion. We show that the sets of ill-posed problems for matrix inversion, eigen-problems, and polynomial zero finding all have a common algebraic and geometric structure which lets us compute the probability distribution of the distance from a “random” problem to the set. From this probability distribution we derive, for example, the distribution of the condition number of a random matrix. We examine the relevance of this theory to the analysis and construction of numerical algorithms destined to be run in finite precision arithmetic." @default.
• W2007175576 created "2016-06-24" @default.
• W2007175576 creator A5076825233 @default.
• W2007175576 date "1987-06-01" @default.
• W2007175576 modified "2023-10-18" @default.
• W2007175576 title "The geometry of III-conditioning" @default.
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• W2007175576 doi "https://doi.org/10.1016/0885-064x(87)90027-6" @default.
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