Pollard’s Monte Carlo factorization algorithm usually finds a factor of a composite integer N in O(N1/4) arithmetic operations. The algorithm is based on a cycle-finding algorithm of Floyd. We describe a cycle-finding algorithm which is about 36 percent faster than Floyd’s (on the average), and apply it to give a Monte Carlo factorization algorithm which is similar to Pollard’s but about 24 per...

In this talk we indicate how elementary number-theoretic results depending on unique factorization can occasionally be established by “differentiating” integers. The presentation is intended to serve as an introduction to differential algebra, and is kept at a very elementary level: no background in that area is assumed, and unique factorization is thoroughly reviewed. For deep connections betw...

— This work proposes a novel method of matrix factorization on the complex domain to obtain both intuitive features and high recognition results in a face recognition system. The real data matrix is transformed into a complex number based on the Euler representation of complex numbers. Base complex matrix factorization (CMF) is developed and two extensions including sparse complex matrix factor...

We develop a computationally less expensive alternative to the direct solution of a large sparse symmetric positive definite system arising from the numerical solution of elliptic partial differential equation models. Our method, substituted factorization , replaces the computationally expensive factorization of certain dense submatrices that arise in the course of direct solution with sparse C...

Spectral factorization plays an important role in many applications such as Wiener filter design, prediction, and estimation. It is known that spectral factorization is a non-continuous mapping on the space of all non-negative continuous functions, satisfying the Paley-Wiener condition. Additionally, it will be shown in this paper that every continuous spectrum is a discontinuity point of the s...

in this paper, we study the arens regularity properties of module actions and we extend some proposition from baker, dales, lau and others into general situations. we establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. in 1951 arens shows that the second dual of banach algebra endowed with the e...

A square factorization of a string w is a factorization of w in which each factor is a square. Dumitran et al. [SPIRE 2015, pp. 54-66] showed how to find a square factorization of a given string of length n in O(n logn) time, and they posed a question whether it can be done in O(n) time. In this paper, we answer their question positively, showing an O(n)-time algorithm for square factorization ...

The problem of efficiently applying a kernel-induced feature space factorization to a largescale data sets is addressed in this thesis. Kernel matrix factorization methods have showed good performances solving machine learning and data analysis problems. However, the present growth of the amount of information available implies the problems can not be solved with conventional methods, due their...