Absolute value preconditioning for symmetric indefinite linear systems

We introduce a novel strategy for constructing symmetric positive definite (SPD) preconditioners for linear systems with symmetric indefinite matrices. The strategy, called absolute value preconditioning, is motivated by the observation that the preconditioned minimal residual method with the inverse of the absolute value of the matrix as a preconditioner converges to the exact solution of the system in at most two steps. Neither the exact absolute value of the matrix nor its exact inverse are computationally feasible to construct in general. However, we provide a practical example of an SPD preconditioner that is based on the suggested approach. In this example we consider a model problem with a shifted discrete negative Laplacian, and suggest a geometric multigrid (MG) preconditioner, where the inverse of the matrix absolute value appears only on the coarse grid, while operations on finer grids are based on the Laplacian. Our numerical tests demonstrate practical effectiveness of the new MG preconditioner, which leads to a robust iterative scheme with minimalist memory requirements

Metal-Insulator Transition in 2D: Experimental Test of the Two-Parameter Scaling

We report a detailed scaling analysis of resistivity \rho(T,n) measured for several high-mobility 2D electron systems in the vicinity of the 2D metal-insulator transition. We analyzed the data using the two parameter scaling approach and general scaling ideas. This enables us to determine the critical electron density, two critical indices, and temperature dependence for the separatrix in the self-consistent manner. In addition, we reconstruct the empirical scaling function describing a two-parameter surface which fits well the \rho(T,n) data.Comment: 4 pages, 4 figures, 1 tabl

Methodology for building the optimal test bench of software and hardware complexes of control systems

The paper considers the issue of creating unified approaches to building test stands for software and hardware control systems. A universal architecture of the test bench is proposed and the author's method of constructing optimal test stands, obtained as a result of research in the field of complex automation of the test process, is described. The algorithm of directed search for the best test stand configuration is considered by example and the results of the implementation of the proposed method are demonstrated. © Published under licence by IOP Publishing Ltd

System analysis and processing of parameters of the test bench

The paper deals with the analysis of complex technical objects - test stands of control systems. A method is proposed for evaluating the effectiveness of the test bench based on the parameters obtained using the "standard"and "automated"test stand model. The objective function for calculating the efficiency of test benches based on their parameters and determining the numerical efficiency coefficient of the testing position relative to the typical one is given. The composition of the software for implementing the proposed method is shown. © Published under licence by IOP Publishing Ltd

Renormalization of hole-hole interaction at decreasing Drude conductivity

The diffusion contribution of the hole-hole interaction to the conductivity is analyzed in gated GaAs/In$_x$Ga$_{1-x}$As/GaAs heterostructures. We show that the change of the interaction correction to the conductivity with the decreasing Drude conductivity results both from the compensation of the singlet and triplet channels and from the arising prefactor $\alpha_i<1$ in the conventional expression for the interaction correction.Comment: 6 pages, 5 figure