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...

Markov chains are one of the most important kinds of models in Simulation. A fast iterative algorithm for the steady state solution of continuous-time Markov chains (CTMCs) was introduced by Horton and Leutenegger [HL94]. The so-called multi-level algorithm utilizes ideas from algebraic multigrid to provide an efficient alternative to the currently used Gauss-Seidel and successive overrelaxatio...

A coupled pair of harmonic equations is solved by the application of Chebyshev acceleration to the Jacobi, Gauss-Seidel, and related iterative methods, where the Jacobi iteration matrix has purely imaginary (or zero) eigenvalues. Comparison is made with a block SOR method used to solve the same problem. Introduction. In [4], we proposed a general block SOR method for solving the biharmonic equa...

In this paper, we present Gauss-Sidel and successive over relaxation (SOR) iterative methods for finding the approximate solution system of fuzzy Sylvester equations (SFSE), AX + XB = C, where A and B are two m*m crisp matrices, C is an m*m fuzzy matrix and X is an m*m unknown matrix. Finally, the proposed iterative methods are illustrated by solving one example.

In this paper, we analyze the potential of using weights for block-asynchronous relaxation methods on GPUs. For this purpose, we introduce different weighting techniques similar to those applied in block-smoothers for multigrid methods. Having proven a sufficient convergence condition for the weighted block-asynchronous iteration, we analyze the performance of the algorithms implemented using C...

In this paper, we present a new iterative rounding framework for many clustering problems. Using this, we obtain an (α1 + ≤ 7.081 + )-approximation algorithm for k-median with outliers, greatly improving upon the large implicit constant approximation ratio of Chen [16]. For k-means with outliers, we give an (α2 + ≤ 53.002 + )-approximation, which is the first O(1)-approximation for this problem...

In this paper, we develop and analyze an efficient multigrid method to solve the finite element systems from elliptic obstacle problems on two dimensional adaptive meshes. Adaptive finite element methods (AFEMs) based on local mesh refinement are an important and efficient approach when the solution is non-smooth. An optimality theory on AFEM for linear elliptic equations can be found in Nochet...

The eigenvalue problem Ax = \Bx, where A and B are large and sparse symmetric matrices, is considered. An iterative algorithm for computing the smallest eigenvalue and its corresponding eigenvector, based on the successive overrelaxation splitting of the matrices, is developed, and its global convergence is proved. An expression for the optimal overrelaxation factor is found in the case where A...

For small number of equations, systems of linear (and sometimes nonlinear) equations can be solved by simple classical techniques. However, for large number of systems of linear (or nonlinear) equations, solutions using classical method become arduous. On the other hand evolutionary algorithms have mostly been used to solve various optimization and learning problems. Recently, hybridization of ...

In this work, we use a symbolic algebra package to derive a family of nite diierence approximations for the biharmonic equation on a 9 point compact stencil. The solution and its rst derivatives are carried as unknowns at the grid points. Dirichlet boundary conditions are thus incorporatednaturally. Since the approximations use the 9 point compact stencil, no special formulas are needed near th...