相关论文: A Computational Algorithm for /pi(N)
In a previous paper a new approach has been introduced for computing, recursively and numerically, one-loop tensor integrals. Here we describe a few modifications of the original method that allow a more efficient numerical implementation…
This article presents an efficient algorithm to generate a discrete uniform distribution on a set of $p$ elements using a biased random source for $p$ prime. The algorithm generalizes Von Neumann's method and improves computational…
We present an algorithm which computes the Landau constant up to any given precision.
With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) and/or diameter (maximum side-length), up to congruence. As we will see, this problem is considerably more difficult than the corresponding…
In this article we use theoretical and numerical methods to evaluate in a closed-exact form the parameters of Ramanujan type $1/\pi$ formulas.
For natural and artificial systems with some symmetry structure, computational understanding and manipulation can be achieved without learning by exploiting the algebraic structure. Here we describe this algebraic coordinatization method…
We use a method of translation to recover Borweins' quadratic and quartic iterations. Then, by using the WZ-method, we obtain some initial values which lead to the limit $1/\pi$. We will not use the modular theory nor either the Gauss'…
The mathematical constant pi has recently been computed up to 22,459,157,718,361 decimal and 18,651,926,753,033 hexadecimal digits. As a simple check for the normality of pi, the frequencies of all sequences with length one, two and three…
In this paper we give another proof of the Chudnovsky formula for calculating $\pi$ - a proof in detail with means of basic complex analysis. With the exception of the tenth chapter, the proof is self-contained, with proofs provided for all…
Let $p$ be an odd prime and $R$ a $p$-torsion-free commutative $\mathbb{Z}_{(p)}$-algebra. We compute the periodic cyclic homology over $R$ of the universal differential graded algebra $R//p$ which is obtained from $R$ by universally…
Approximate Counting refers to the problem where we are given query access to a function $f : [N] \to \{0,1\}$, and we wish to estimate $K = #\{x : f(x) = 1\}$ to within a factor of $1+\epsilon$ (with high probability), while minimizing the…
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating…
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the…
In our earlier publication we have shown how to compute by iteration a rational number ${u_{2,k}}$ in the two-term Machin-like formula for pi of kind…
The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities by reducing to polynomial inequalities. Finally, we show the great applicability of this algorithm and as examples, we use it to…
Some variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term numerical emphasizes that a numerical solution is computed. The method consists in replacing the right hand…
Let $f$ be a fixed (holomorphic or Maass) modular cusp form. Let $\cq$ be a Dirichlet character mod $q$. We describe a fast algorithm that computes the value $L(1/2,f\times\chi_q)$ up to any specified precision. In the case when $q$ is…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…