منابع مشابه
On Euclidean norm approximations
Euclidean norm calculations arise frequently in scientific and engineering applications. Several approximations for this norm with differing complexity and accuracy have been proposed in the literature. Earlier approaches [1, 2, 3] were based on minimizing the maximum error. Recently, Seol and Cheun [4] proposed an approximation based on minimizing the average error. In this paper, we first exa...
متن کاملNorm Euclidean Quaternionic Orders
We determine the norm Euclidean orders in a positive definite quaternion algebra over Q. Lagrange (1770) proved the four square theorem via Euler’s four square identity and a descent argument. Hurwitz [4] gave a quaternionic proof using the order Λ(2) with Z-basis: 1, i, j, 1 2 (1 + i + j + k). Here i = j = −1 and ij = −ji = k, the standard basis of the quaternions. The key property of Λ(2) is ...
متن کاملNorm-euclidean Cyclic Fields of Prime Degree
Let K be a cyclic number field of prime degree `. Heilbronn showed that for a given ` there are only finitely many such fields that are normEuclidean. In the case of ` = 2 all such norm-Euclidean fields have been identified, but for ` 6= 2, little else is known. We give the first upper bounds on the discriminants of such fields when ` > 2. Our methods lead to a simple algorithm which allows one...
متن کاملOn Extremes of Multidimensional Stationary Diffusion Processes in Euclidean Norm
Let (Xt)t≥0 be a R-valued stationary reversible diffusion process. We investigate the asymptotic behavior of MT := max0≤t≤T |Xt|, where | · | is the Euclidean norm in R. The aim of this paper is to characterize the tail asymptotics of MT for fixed T > 0 as well as the long time behavior of MT as T → ∞. This is related to spectral asymptotics of the generator of (Xt)t≥0 subject to Dirichlet boun...
متن کاملPlanar Separators and the Euclidean Norm
In this paper we show that every 2-connected embedded planar graph with faces of sizes d! . . . . . df has a simple cycle separator of size 1.58~,/dl 2 + . . . + d } and we give an almost linear time algorithm for finding these separators, O(m~(n. n)). We show that the new upper bound expressed as a function of IG{ = ~/d~ +..+ d} is no larger, up to a constant factor than previous bounds that w...
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ژورنال
عنوان ژورنال: Pattern Recognition
سال: 2011
ISSN: 0031-3203
DOI: 10.1016/j.patcog.2010.08.028