A subquadratic algorithm for computing the n-th Bernoulli number

نویسنده

  • David Harvey
چکیده

We describe a new algorithm that computes the nth Bernoulli number in n4/3+o(1) bit operations. This improves on previous algorithms that had complexity n2+o(1).

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Akiyama-Tanigawa algorithm for Bernoulli numbers

A direct proof is given for Akiyama and Tanigawa’s algorithm for computing Bernoulli numbers. The proof uses a closed formula for Bernoulli numbers expressed in terms of Stirling numbers. The outcome of the same algorithm with different initial values is also briefly discussed. 1 The Algorithm In their study of values at non-positive integer arguments of multiple zeta functions, S. Akiyama and ...

متن کامل

Approximation of the n-th Root of a Fuzzy Number by Polynomial Form Fuzzy Numbers

In this paper we introduce the root of a fuzzy number, and we present aniterative method to nd it, numerically. We present an algorithm to generatea sequence that can be converged to n-th root of a fuzzy number.

متن کامل

On Approximating Addition by Exclusive OR

Let X, X, . . . , X be independent and uniformly distributed over the non-negative integers {0, 1, . . . , 2 − 1}; S = X +X + · · ·+X and L = X ⊕X ⊕ · · · ⊕X. Denote the i-th bits of S and L by S i and L (n) i respectively. We show that as i→∞, Pr[S (n) i = L (n) i ]→ γ = 1 2 + 2n+1(2n+1−1) 2(n+1) × bn+1 n! , where bn is the n-th Bernoulli number. As a consequence, γ (2r) = 1/2 for every r; and...

متن کامل

Selection in Monotone Matrices and Computing kth Nearest Neighbors

' ŽŽ . . We present an O m q n n log n time algorithm to select the k th smallest item from an m = n totally monotone matrix for any k F mn. This is the first subquadratic algorithm for selecting an item from a totally monotone matrix. Our method also yields an algorithm of the same time complexity for a generalized 4 row-selection problem in monotone matrices. Given a set S s p , . . . , p of ...

متن کامل

Taking Roots over High Extensions of Finite Fields

We present a new algorithm for computing m-th roots over the finite field Fq, where q = pn, with p a prime, and m any positive integer. In the particular case m = 2, the cost of the new algorithm is an expected O(M(n) log(p) + C(n) log(n)) operations in Fp, where M(n) and C(n) are bounds for the cost of polynomial multiplication and modular polynomial composition. Known results give M(n) = O(n ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Math. Comput.

دوره 83  شماره 

صفحات  -

تاریخ انتشار 2014