The results of the pilot study of exposure to airborne particles and polycyclic aromatic hydrocarbons (PAHs) close to a busy street in Gliwice in the spring are presented. Traffic density in the ...investigated street between 9 a.m. and 6 p.m. was 1400 vehicles per hour. It was found that average daily concentration of PM10 (airborne particles with aerodynamic diameter < 10 mu m) increases by 40 mu g/m super(3) in the street canyon in relation to locations 100 m from the road, which for inhabitants who live in this street means an increased of risk of respiratory diseases by ten percent. The average concentration of total PAHs near the street was 191.56 ng/m super(3) (in the spring and without rain) and was over 1.5 times greater than at the point 100 m from the street, which confirms that exhaust gases emission on busy streets elevates the exposure to total PAHs. However, it does not concern benzo(a)pyrene (BaP), whose main emission sources seem to be industrial and municipal emitters. Exposure to BaP concerns not only the persons who live close to the busy streets, but the greater population of the Gliwice inhabitants. The risk of cancer diseases in the studied area associated with inhalation of aerosol particles containing BaP is 10 super(-4), but persons living in the investigated street have a higher cancer risk of 10 super(-3) order.
We investigate condition numbers of matrices that appear during solving systems of linear equations. We consider iterative methods to solve the equations, namely Jacobi and Gauss-Seidel methods. We ...examine the influence of the condition number on convergence of these iterative methods. We study numerical aspects of relations between the condition number and the size of the matrix and the number of iterations experimentally. We analyze random matrices, the Hilbert matrix and a strictly diagonally dominant matrix.
We present a novel implementation of a dense, square, non-structured matrix factorization algorithm, namely the WZ factorization - with the use of graphics processors (GPUs) and CPUs to gain a high ...performance at a low cost. We rewrite this factorization as operations on blocks of matrices and vectors. We have implemented our block-vector algorithm on GPUs with the use of an appropriate (and ready-to-use) GPU-accelerated mathematical library, namely the CUBLAS library. We compared the performance of our algorithm with CPU implementations. In particular, our implementation on an NVIDIA Tesla C2050 GPU outperforms a CPU-based implementation. Our results show that the algorithm scales well with the size of matrices; moreover, the larger the matrix, the better the performance. We also discuss the impact of the size of the matrix and the use of ready-to-use mathematical libraries on the numerical accuracy.
Markovian models can generate very large sparse matrices, which are difficult to store and solve. A useful method for finding transient probabilities in Markovian models is the uniformization. The ...aim of this paper is to show that the performance of the uniformization can be improved using multi-GPU architecture. We propose partitioning scheme for HYB sparse matrix storage format and some optimization techniques adjusted so as to minimize communication between GPUs during iterative sparse matrix-vector multiplication, which is the most time consuming step. The results of experiments show that on multi-GPU we can solve larger matrices than on single device and accelerate computations in comparison to a multithreaded CPU. Computational test have been carried out in double precision for a wireless network models. Using multi-GPU we were able to solve model which is described by a matrix of the size 3.6×10 7 .
This paper is a review and a comparison of some preconditioners based on incomplete factorizations of matrices - for matrices describing Markov chains. Three preconditioners are considered: ILU(0), ...ILU3, IWZ(0). Two of them (ILU(0), ILU3) are based on the LU factorization, the latter (IWZ(0)) - on the WZ factorization. The preconditioners are investigated in respect of their usability for decreasing number of iterations in a projection method, namely GMRES(m). To chose the best preconditioner for such methods, authors introduce a measure called iteration speed-up (p) and some of its relatives, as well as they define a function giving an average number of restarts needed to achieve a given accuracy for matrices from a some set (Is). These measures are studied for two different cases of matrices describing Markov chains to compare influence of the examined incomplete preconditioners for GMRES(m).
The authors consider the impact of the structure of the matrix on the convergence behavior for the GMRES projection method for solving large sparse linear equation systems resulting from Markov ...chains modeling. Studying experimental results we investigate the number of steps and the rate of convergence of GMRES method and the IWZ preconditioning for the GMRES method. The motivation is to better understand the convergence characteristics of Krylov subspace method and the relationship between the Markov model, the nonzero structure of the coefficient matrix associated with this model and the convergence of the preconditioned GMRES method.
The authors consider the use of the parallel iterative methods for solving large sparse linear equation systems resulting from Markov chains-on a computer cluster. A combination of Jacobi and ...Gauss-Seidel iterative methods is examined in a parallel version. Some results of experiments for sparse systems with over 3 times 10 7 equations and about 2 times 10 8 nonzeros which we obtained from a Markovian model of a congestion control mechanism are reported.
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