相关论文: Modular Multiplication without Carry Propagation (…

We present a highly scalable algorithm for multiplying sparse multivariate polynomials represented in a distributed format. This algo- rithm targets not only the shared memory multicore computers, but also computers clusters or specialized…

We show that Boolean matrix multiplication, computed as a sum of products of column vectors with row vectors, is essentially the same as Warshall's algorithm for computing the transitive closure matrix of a graph from its adjacency matrix.…

We present a new probabilistic algorithm to compute modular polynomials modulo a prime. Modular polynomials parameterize pairs of isogenous elliptic curves and are useful in many aspects of computational number theory and cryptography. Our…

Binary addition is one of the most primitive and most commonly used applications in computer arithmetic. A large variety of algorithms and implementations have been proposed for binary addition. Huey Ling proposed a simpler form of CLA…

Polynomial multiplication is known to have quasi-linear complexity in both the dense and the sparse cases. Yet no truly linear algorithm has been given in any case for the problem, and it is not clear whether it is even possible. This…

We propose a Fourier-based learning algorithm for highly nonlinear multiclass classification. The algorithm is based on a smoothing technique to calculate the probability distribution of all classes. To obtain the probability distribution,…

This paper shows how to design efficient arithmetic elements out of quantum gates using "carry-save" techniques borrowed from classical computer design. This allows bit-parallel evaluation of all the arithmetic elements required for Shor's…

We present an algorithm to perform a simultaneous modular reduction of several residues. This algorithm is applied fast modular polynomial multiplication. The idea is to convert the $X$-adic representation of modular polynomials, with $X$…

Recently there has been quite a bit of study carried out related to arithmetic properties of overpartitions into non-multiples of two co-prime integers. The paper [19] by Nadji et al. looked into congruences modulo $3$ and powers of $2$ for…

The multiplicative (or geometric) calculus is a non-Newtonian calculus derived from an arithmetic in which the operations of addition/subtraction/multiplication are replaced by multiplication/division/exponentiation. A major difference…

This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…

Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The…

In this paper we propose a novel algorithm to combine two or more cellular complexes, providing a minimal fragmentation of the cells of the resulting complex. We introduce here the idea of arrangement generated by a collection of cellular…

This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be…

By double ideal quotient, we mean $(I:(I:J))$ where ideals $I$ and $J$. In our previous work [11], double ideal quotient and its variants are shown to be very useful for checking prime divisor and generating primary component. Combining…

In this note, we revisit the algorithm of Har-Peled et. al. [HRZ07] for computing a linear maximum margin classifier. Our presentation is self contained, and the algorithm itself is slightly simpler than the original algorithm. The…

In this paper, we propose an extension to the Propagator algorithm for source bearing estimation by performing root decomposition which eliminates the need for spectral search over angles. Further the propagator spatial spectrum is reused…

We present the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. Given a system of differential equations possessing conservation laws, our approach is based on…

We study the existence of the product of two weighted modulation spaces. For this purpose we discuss two different strategies. The more simple one allows transparent proofs in various situations. However, our second method allows a closer…

Several approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a supervised learning problem, have been proposed recently. Finding good policies…