The Square Root Normal Field Distance and Unbalanced Optimal Transport

Eulerian models and algorithms for unbalanced optimal transport

Optimal Reparametrizations in the Square Root Velocity Framework

The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to the quotient space of unparametrised curves. In this paper we study analytical and topological aspects of this construction for the class of absolutely continuous curves. We show that the square root veloc...

Square Root Algorithms for the Number Field Sieve

We review several methods for the square root step of the Number Field Sieve, and present an original one, based on the Chinese Remainder Theorem. We consider in this article the final step of the Number Field Sieve (NFS) factoring algorithm [3], namely the algebraic square root computation. This problem is stated as follows. Let K = Q(α) be a number field, where α is defined as a root of the i...

A Montgomery-Like Square Root for the Number Field Sieve

The Number Field Sieve (NFS) is the asymptotically fastest factoring algorithm known. It had spectacular successes in factoring numbers of a special form. Then the method was adapted for general numbers, and recently applied to the RSA-130 number [6], setting a new world record in factorization. The NFS has undergone several modifications since its appearance. One of these modifications concern...

On the square root of quadratic matrices

Here we present a new approach to calculating the square root of a quadratic matrix. Actually, the purpose of this article is to show how the Cayley-Hamilton theorem may be used to determine an explicit formula for all the square roots of $2times 2$ matrices.