Fast Cadzow’s Algorithm and a Gradient Variant

A New Fast Data Encryption Algorithm (FDE)

Fast quantum algorithm for numerical gradient estimation.

Given a black box for f, a smooth real scalar function of d real variables, one wants to estimate [symbol: see text]f at a given point with n bits of precision. On a classical computer this requires a minimum of d + 1 black box queries, whereas on a quantum computer it requires only one query regardless of d. The number of bits of precision to which f must be evaluated matches the classical req...

A New Fast Data Encryption Algorithm (FDE)

A fast variant of the Gaussian reduction algorithm

We propose a fast variant of the Gaussian algorithm for the reduction of two– dimensional lattices for the l1−, l2− and l∞−norm. The algorithm runs in at most O(nM(B) log B) bit operations for the l∞−norm and in O(n log n M(B) log B) bit operations for the l1− and l2−norm on input vectors a, b ∈ ZZ with norm at most 2 where M(B) is a time bound for B-bit integer multiplication. This generalizes...

A Fast Distributed Stochastic Gradient Descent Algorithm for Matrix Factorization

The accuracy and effectiveness of matrix factorization technique were well demonstrated in the Netflix movie recommendation contest. Among the numerous solutions for matrix factorization, Stochastic Gradient Descent (SGD) is one of the most widely used algorithms. However, as a sequential approach, SGD algorithm cannot directly be used in the Distributed Cluster Environment (DCE). In this paper...