相关论文: A Computational Algorithm for /pi(N)
An NP-hard combinatorial optimization problem $\Pi$ is said to have an {\em approximation threshold} if there is some $t$ such that the optimal value of $\Pi$ can be approximated in polynomial time within a ratio of $t$, and it is NP-hard…
In this paper we propose a new method for determination of the two-term Machin-like formula for pi with arbitrarily small arguments of the arctangent function. This approach excludes irrational numbers in computation and leads to a…
In this article, we develop nested representations for cosine and inverse cosine functions, which is a generalization of Vi\`{e}te's formula for $\pi$. We explore a natural inverse relationship between these representations and develop…
We present a distributed algorithm to compute the first homology of a simplicial complex. Such algorithms are very useful in topological analysis of sensor networks, such as its coverage properties. We employ spanning trees to compute a…
We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.
Every human likes choices. But today's fast route planning algorithms usually compute just a single route between source and target. There are beginnings to compute alternative routes, but this topic has not been studied thoroughly. Often,…
Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…
A semiprime is a natural number which can be written as the product of two primes. The asymptotic behaviour of the function $\pi_2(x)$, the number of semiprimes less than or equal to $x$, is studied. Using a combinatorial argument,…
The aim of this paper is to generalize the algorithm to compute jumping numbers on rational surfaces described in [AAD14] to varieties of dimension at least 3. Therefore, we introduce the notion of $\pi$-antieffective divisors, generalizing…
We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is…
We consider the problem of computing the nearest matrix polynomial with a non-trivial Smith Normal Form. We show that computing the Smith form of a matrix polynomial is amenable to numeric computation as an optimization problem.…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
In this paper, we suggest a new efficient algorithm in order to compute S-polynomial reduction rapidly in the known algorithm for computing Grobner bases, and compare the complexity with others.
Ordinary Differential Equations are generally too complex to be solved analytically. Approximations thereof can be obtained by general purpose numerical methods. However, even though accurate schemes have been developed, they remain…
We present an algorithm to estimate the configurational entropy $S$ of a polymer. The algorithm uses the statistics of coincidences among random samples of configurations and is related to the catch-tag-release method for estimation of…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…
In this paper, we calculate an exact formula for the number of partitions of a natural number $n$, where the largest part is even and no odd parts appears more than two times. The generating functions of the number of these partitions is a…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
In this paper we propose an algorithm that correctly discards a set of numbers (from a previously defined sieve) with an interval of integers. Leopoldo's Theorem states that the remaining integer numbers will generate and count the complete…