Related papers: A fast amortized algorithm for computing quadratic…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
In recent years there has been a renewed interest in finding fast algorithms to compute accurately the linear canonical transform (LCT) of a given function. This is driven by the large number of applications of the LCT in optics and signal…
We present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the algorithm is equivalent to non-factorizability for which we…
We introduce a fast algorithm to compute the Ramanujan-Deninger gamma function and its logarithmic derivative at positive values. Such an algorithm allows us to greatly extend the numerical investigations about the Euler-Kronecker constants…
It is well known that the repeated square and multiply algorithm is an efficient way of modular exponentiation. The obvious question to ask is if this algorithm has an inverse which would calculate the discrete logarithm efficiently. The…
In this paper we consider the distribution of large central values of Dirichlet L-functions over cosets of the group of characters modulo q via Soundararajan's resonator method.
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.
In the present work, we present a new discrete logarithm algorithm, in the same vein as in recent works by Joux, using an asymptotically more efficient descent approach. The main result gives a quasi-polynomial heuristic complexity for the…
Recently, there has been a surge of interest for quantum computation for its ability to exponentially speed up algorithms, including machine learning algorithms. However, Tang suggested that the exponential speed up can also be done on a…
In this paper, we design, analyze, and implement a variant of the two-loop L-shaped algorithms for solving two-stage stochastic programming problems that arise from important application areas including revenue management and power systems.…
Fast algorithms for arithmetic on real or complex polynomials are well-known and have proven to be not only asymptotically efficient but also very practical. Based on Fast Fourier Transform (FFT), they for instance multiply two polynomials…
A distributed algorithm is described for solving a linear algebraic equation of the form $Ax=b$ assuming the equation has at least one solution. The equation is simultaneously solved by $m$ agents assuming each agent knows only a subset of…
Some Dirichlet-like functions, attached to a pair (periodic function, polynomial) are introduced and studied. These functions generalize the standard Dirichlet L-functions of Dirichlet characters. They have similar properties, being…
We establish lower bounds for the $2k$-th moment of families of quadratic Dirichlet $L$-functions at the central point for all real $k<0$, assuming a conjecture of S. Chowla on the non-vanishing of these $L$-values.
I would like to tell a story. A story about a beautiful mathematical relationship that elucidates the computational view on the classic subject of trigonometry. All stories need a language, and for this particular story an algorithmic…
In this paper, we establish the expected order of magnitude of the $k$th-moment of quadratic Dirichlet $L$-functions associated to hyperelliptic curves of genus $g$ as well as of prime moduli over a fixed finite field $\mathbb{F}_{q}$ for…
This article aims to find explicit congruences between Dirichlet characters and gives various results on how to find some effectively on a computer. It ends with concrete examples putting those ideas in application.
Solving linear diophantine equations in two variables have applications in computer science and mathematics. In this paper, we revisit an algorithm for solving linear diophantine equations in two variables, which we refer as DEA-R…
The paper deals with the problem of approximating the functions of several variables by branched continued fractions, in particular, multidimensional A- and J-fractions with independent variables. A generalization of Gragg's algorithm is…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…