Problem statement: A new variant of the Successive Overrelaxation (SOR) method for solving linear algebraic systems, the KSOR method was introduced. The treatment depends on the assumption that the current component can be used simultaneously in the evaluation in addition to the use the most recent calculated components as in the SOR method. Approach: Using the hidden explicit characterization ...

Successive over-relaxation (SOR) is a computationally intensive, yet extremely important iterative solver for solving linear systems. Due to recent trends of exponential growth in amount of data generated and increasing problem sizes, serial platforms have proved to be insufficient in providing the required computational power. In this paper, we present parallel implementations of red-black SOR...

We study the complete set packing problem (CSPP) where the family of feasible subsets may include all possible combinations of objects. This setting arises in applications such as combinatorial auctions (for selecting optimal bids) and cooperative game theory (for finding optimal coalition structures). Although the set packing problem has been well-studied in the literature, where exact and app...

We study several network design problems with degree constraints. For the degree-constrained 2-connected subgraph problem we obtain a factor 6 violation for the degrees with 4 approximation for the cost. This improves upon the logarithmic degree violation and no cost guarantee obtained by Feder, Motwani, and Zhu (2006). Then we consider the problem of finding an arborescence with at least k ter...

Split cuts constitute a class of cutting planes that has been successfully employed by the majority of Branch-and-Cut solvers for Mixed Integer Linear Programs. Given a basis of the LP relaxation and a split disjunction, the corresponding split cut can be computed with a closed form expression. In this paper, we use the Lift-and-Project framework [10] to provide the basis, and the Reduce-andSpl...

{(f1(x), . . . , fm(x)) : x ∈ T } for quadratic polynomials f0, . . . , fm and a subset T of R . This paper studies semidefinite representation of the convex hull conv(V ) or its closure, i.e., describing conv(V ) by projections of spectrahedra (defined by linear matrix inequalities). When T is defined by a single quadratic constraint, we prove that conv(V ) is equal to the first order moment t...

Introduction: A promising approach for the simultaneous quantification of proton density, T1 and T2 is the IR TrueFISP sequence proposed by Schmitt et al. [1]. This sequence consists of an inversion pulse followed by a series of TrueFISP acquisitions, observing a quasirelaxation towards the steady-state. However, this sequence requires a delay between individual segments in order to allow the m...

In order to understand the origin of stock price jumps, we crosscorrelate high-frequency time series of stock returns with different news feeds. We find that neither idiosyncratic news nor market wide news can explain the frequency and amplitude of price jumps. We find that the volatility patterns around jumps and around news are quite different: jumps are followed by increased volatility, wher...

The spin-lattice relaxation times for the In isotope in liquid indium embedded into artificial opals and porous glass were found to be shortened remarkably compared to the bulk indium melt. The spin relaxation acceleration was ascribed mainly to the enhancement of the quadrupole contribution caused by the translational diffusion in liquid indium; the magnetic contribution was implied unchanged ...

A two-dimensional numerical model was developed to determine the effect of the non-Newtonian behavior of blood on a pulsatile flow at the aortic bifurcation. The blood rheology was described by a weak-form Casson equation. The successive-over-relaxation (SOR) method was used to solve both the vorticity and Poisson equations numerically. It was disclosed that the non-Newtonian property of blood ...