We study in this article both the structure and the structural evolution of the solutions of 2-D Navier-Stokes equations with periodic boundary conditions and the evolution of their solutions. First the structure of all eigenvectors of the corresponding Stokes problem is classified using a block structure, and is linked to the typical structure of the Taylor vortices. Then the structure of the ...

Algebraic attacks lead to the task of solving polynomial systems over F2. We study recent suggestions of using SAT-solvers for this task. In particular, we develop several strategies for converting the polynomial system to a set of CNF clauses. This generalizes the approach in [4]. Moreover, we provide a novel way of transforming a system over F2e to a (larger) system over F2. Finally, the effi...

The randomized Kaczmarz algorithm has received considerable attention recently because of its simplicity, speed, and the ability to approximately solve large-scale linear systems equations. In this paper we propose double triple algorithms extended normal equations form $$\mathbf{A}^\top \mathbf{Ax}=\mathbf{A}^\top \mathbf{b}-\mathbf{c}$$ . proposed avoid forming \mathbf{A}$$ explicitly work fo...

Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very problems, iterative solver needed and, in general, a preconditioner required achieve good convergence. In recent years, number of preconditioners have been proposed. These are largely serial, reported results demonstrate that none commonly used for matrix ca...