Asymptotic semismoothness probabilities
نویسندگان
چکیده
منابع مشابه
Asymptotic semismoothness probabilities
We call an integer semismooth with respect to y and z if each of its prime factors is ≤ y, and all but one are ≤ z. Such numbers are useful in various factoring algorithms, including the quadratic sieve. Let G(α, β) be the asymptotic probability that a random integer n is semismooth with respect to nβ and nα. We present new recurrence relations for G and related functions. We then give numerica...
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Any spectral function can be written as a composition of a symmetric function f : IR 7→ IR and the eigenvalue function λ(·) : S 7→ IR, often denoted by (f ◦ λ), where S is the subspace of n×n symmetric matrices. In this paper, we present some nonsmooth analysis for such spectral functions. Our main results are: (a) (f ◦ λ) is directionally differentiable if f is semidifferentiable; (b) (f ◦ λ) ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1996
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-96-00775-2