In this work we consider the Successive Overrelaxation (SOR) method for the solution of a linear system Ax = b, when the matrix A has a block p X P partitioned p-cyclic form and its associated block Jacobi matrix Jp 1s weaJdy cyclic of index p. Following the pioneering work by Young and Varga in the 50s many researchers have considered various cases for the spectrum 0'(Jp ) and have determlned ...

Thermochemical relaxation behind a normal shock in Mars and Titan gas mixtures is simulated using a CFD solver, DPLR, for a hemisphere of 1 m radius; the thermochemical relaxation along the stagnation streamline is considered equivalent to the flow behind a normal shock. Flow simulations are performed for a Titan gas mixture (98% N2, 2% CH4 by volume) for shock speeds of 5.7 and 7.6 km/s and pr...

This problem is NP-hard, so there is no known algorithm to determine the solution in polynomial time. Instead we seek to compute an approximate solution in polynomial time. One strategy for accomplishing this, first pioneered by Goemans & Williamson in Ref. [3], is to employ a semidefinite relaxation. This technique consists of three steps: first construct a related problem that is a semidefini...

Linear programming (LP) relaxations are widely used to attempt to identify a most likely configuration of a discrete graphical model. In some cases, the LP relaxation attains an optimum vertex at an integral location and thus guarantees an exact solution to the original optimization problem. When this occurs, we say that the LP relaxation is tight. Here we consider binary pairwise models and de...

Gomory mixed-integer (GMI) cuts are among the most effective cutting planes for general mixed-integer programs (MIP). They are traditionally generated from an optimal basis of a linear programming (LP) relaxation of a MIP. In this paper we propose a heuristic to generate useful GMI cuts from additional bases of the initial LP relaxation. The cuts we generate have rank one, i.e., they do not use...

We investigated the dynamics of a series of room temperature ionic liquids based on the same 1-butyl-3-methyl imidazolium cation and different anions by means of broadband dielectric spectroscopy covering 15 decades in frequency (10-10Hz), and in the temperature range from 400 K down to 35 K. An ionic conductivity is observed above the glass transition temperature Tg with a relaxation in the el...

A computationally efficient numerical method for the solution of nonlinear sea ice dynamics models employing viscous-plastic rheologies is presented. The method is based on a semi-implicit decoupling of the x and y ice momentum equations into a form having better convergence properties than the coupled equations. While this decoupled form also speeds up solutions employing point relaxation meth...

The paper is concerned with variants of the successive overrelaxation method (SOR method) for solving the linear system Au = b. Necessary and sufficient conditions are given for the convergence of the symmetric and unsymmetric SOR methods when A is symmetric. The modified SOR, symmetric SOR, and unsymmetric SOR methods are also considered for systems of the form DiHt — Cau2 = b¡, — CLui + D2u2 ...