Related papers: Algorithm to Compute Squares of 1st N Natural Numb…
Many large arithmetic computations rely on tables of all primes less than $n$. For example, the fastest algorithms for computing $n!$ takes time $O(M(n\log n) + P(n))$, where $M(n)$ is the time to multiply two $n$-bit numbers, and $P(n)$ is…
In this Letter, we construct the quantum algorithms for the Simon problem and the period-finding problem, which do not require initializing the auxiliary qubits involved in the process of functional evaluation but are as efficient as the…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of…
On the math-fun mailing list (7 May 2013), Neil Sloane asked to calculate the number of $n \times n$ matrices with entries in $\{0,1\}$ which are squares of other such matrices. In this paper we analyze the case that the arithmetic is in…
This paper presents a computer program, written in Maple, that allows a user to simulate certain aspects of Shor's quantum factoring algorithm on a desktop or laptop computer. The program does not simulate the unitary operations carried out…
Several physics-based algorithms for factorizing large number were recently published. A notable recent one by Schleich et al. uses Gauss sums for distinguishing between factors and non-factors. We demonstrate two NMR techniques that…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Pollard's Rho is a method for solving the integer factorization problem. The strategy searches for a suitable pair of elements belonging to a sequence of natural numbers that given suitable conditions yields a nontrivial factor. In…
The aim of this paper is to prove wordlessly the sum formula of $1^{k}+2^{k}+\ldots +n^{k}$, $k\in\{1,2,3\}$.
The scheduling problem consists of finding a common 1 in two remotely located N bit strings. Denote the number of 1s in the string with the fewer 1s by epsilon*N. Classically, it needs at least O(epsilon*N) bits of communication to find the…
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…
This paper presents a distinctive prime detection approach. This method use GM-(n+1) sequences to effectively eliminate complex numbers. The sequences, which consist of odd a number of (n+1), exclude all components except for the initial…
The simplest technique for simulating a quantum algorithm - QA described based on the direct matrix representation of the quantum operators. Using this approach, it is relatively simple to simulate the operation of a QA and to perform…
Non-negative least squares (NNLS) problem is one of the most important fundamental problems in numeric analysis. It has been widely used in scientific computation and data modeling. In big data, the limitations of algorithm speed and…
These lecture notes focus on some numerical linear algebra algorithms in scientific computing. We assume that students are familiar with elementary linear algebra concepts such as vector spaces, systems of equations, matrices, norms,…
This paper presents iterative methods for solving tensor equations involving the T-product. The proposed approaches apply tensor computations without matrix construction. For each initial tensor, these algorithms solve related problems in a…
Magic squares are a fascinating mathematical challenge that has intrigued mathematicians for centuries. Given a positive (and possibly large) integer \( n \), one of the main challenges that still remains is to find, within a computational…
Randomized algorithms in numerical linear algebra can be fast, scalable and robust. This paper examines the effect of sketching on the right singular vectors corresponding to the smallest singular values of a tall-skinny matrix. We analyze…
This paper proposes a general algorithm called Store-zechin for quickly computing the permanent of an arbitrary square matrix. Its key idea is storage, multiplexing, and recursion. That is, in a recursive process, some sub-terms which have…