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Approximate Zeros and Condition Numbers

✍ Scribed by Felipe Cucker

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
134 KB
Volume
15
Category
Article
ISSN
0885-064X

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πŸ“œ SIMILAR VOLUMES

Approximating the Number of Zeroes of a
Approximating the Number of Zeroes of a GF[2] Polynomial
✍ M. Karpinski; M. Luby πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 325 KB

We develop a probabilistic polynomial time algorithm which on input a polynomial \(g\left(x_{1}, \ldots, x_{n}\right)\) over \(G F[2], \epsilon\) and \(\delta\), outputs an approximation to the number of zeroes of \(g\) with relative error at most \(\epsilon\) with probability at least \(1-\delta\).

Uniformly Approximable Numbers and the U
Uniformly Approximable Numbers and the Uniform Approximation Spectrum
✍ Edward B. Burger πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 475 KB

We say a real number : is uniformly approximable if the upper bound in Dirichlet's theorem, from diophantine approximation, of 1Γ‚(Q+1) q may be sharpened to c(:)Γ‚(Q+1) 2 for all sufficiently large Q. Here we begin by showing that the set of uniformly approximable numbers is precisely the set of badl