Related papers: Fast Arithmetics Using Chinese Remaindering
We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained…
We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and…
Numerical solutions for flows in partially saturated porous media pose challenges related to the non-linearity and elliptic-parabolic degeneracy of the governing Richards' equation. Iterative methods are therefore required to manage the…
In this paper we derive and analyse new exponential collocation methods to efficiently solve the cubic Schr\"{o}dinger Cauchy problem on a $d$-dimensional torus. Energy preservation is a key feature of the cubic Schr\"{o}dinger equation. It…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
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…
We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…
Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper…
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear subspace of the field. We view these transforms as performing a change of basis from…
In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…
Chinese input recommendation plays an important role in alleviating human cost in typing Chinese words, especially in the scenario of mobile applications. The fundamental problem is to predict the conditional probability of the next word…
In this paper, we investigate fast algorithms in the small fraction order regime to approximate the Caputo derivative $^C_0D_t^\alpha u(t)$ when $\alpha$ is small. We focus on two fast algorithms, i.e. FIR and FIDR, both relying on the…
We first survey the current state of the art concerning the dynamical properties of multidimensional continued fraction algorithms defined dynamically as piecewise fractional maps and compare them with algorithms based on lattice reduction.…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
This paper detailedly discusses the locally one-dimensional numerical methods for efficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional…
Pronouns are frequently omitted in pro-drop languages, such as Chinese, generally leading to significant challenges with respect to the production of complete translations. Recently, Wang et al. (2018) proposed a novel reconstruction-based…
We show how to improve the efficiency of the computation of fast Fourier transforms over F_p where p is a word-sized prime. Our main technique is optimisation of the basic arithmetic, in effect decreasing the total number of reductions…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
This remark describes efficiency improvements to Algorithm 916 [Zaghloul and Ali 2011]. It is shown that the execution time required by the algorithm, when run at its highest accuracy, may be improved by more than a factor of two. A better…