Many real-world domains contain multiple agents behaving strategically with probabilistic transitions and uncertain (potentially infinite) duration. Such settings can be modeled as stochastic games. While algorithms h...
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With regard to the research on financial risk management, Value-at-Risk(VaR) has been widely accepted as a standard approach to financial risk management. There are various ways applicable to calculate VaR, of which M...
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Determinants has been used intensively in a variety of applications through history. It also influenced many fields of mathematics like linear algebra. Finding the determinants of a squared matrix can be done using a ...
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ISBN:
(纸本)9781479904624
Determinants has been used intensively in a variety of applications through history. It also influenced many fields of mathematics like linear algebra. Finding the determinants of a squared matrix can be done using a variety of methods, including well-known methods of Leibniz formula and Laplace expansion which calculate the determinant of any NxN matrix in O(n!). However, decomposition methods, such as: LU decomposition, Cholesky decomposition and QR decomposition, have replaced the native methods with a significantly reduced complexity of O(n boolean AND 3). In this paper, we introduce two parallel algorithms for Laplace expansion and LU decomposition. Then, we analyze them and compare them with their perspective sequential algorithms in terms of run time, speed-up and efficiency, where new algorithms provided better results. At maximum, in Laplace expansion, it became 129% faster, whereas in LU Decomposition, it became 44% faster.
In this work, we present a WZ factorization for a nonsingular diagonally dominant banded matrix. With little modifications in the structures of W and Z, we construct a stable parallel algorithm suitable for solving na...
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ISBN:
(纸本)9781665410175
In this work, we present a WZ factorization for a nonsingular diagonally dominant banded matrix. With little modifications in the structures of W and Z, we construct a stable parallel algorithm suitable for solving narrow banded nonsingular diagonally dominant linear systems using divide and conquer technique. Partition the coefficient matrix along the main diagonal; also partition the unknown vector and the right hand side vector accordingly. The coefficient matrix of the ‘reduced system’ which is obtained by collecting the first ß and last ß equations from each partition, where ß is semibadwidth of the given banded linear system, is proved to be nonsingular diagonally dominant. The backward error analysis of the algorithm is presented and the algorithm is proved to be numerically stable. Numerical experiments are conducted to check the performance of the parallel algorithm and to compare the present parallel algorithm with the corresponding subroutines of ScaLAPACK. The performance of the parallel algorithm is evaluated in terms of speedup and scalability.
In recent years, filter bank multicarrier (FBMC) has recaptured widespread interests for its possible applications in cognitive radio and dynamic spectrum access. A distinctive feature for cognitive radio is its adapt...
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ISBN:
(纸本)9781467362351
In recent years, filter bank multicarrier (FBMC) has recaptured widespread interests for its possible applications in cognitive radio and dynamic spectrum access. A distinctive feature for cognitive radio is its adaptivity to environment. When environment changes, a cognitive radio will change its parameters to optimize the transmission and receiving. Thus it is desirable to design a unified structure and algorithm for FBMC that needs little change for different parameters. In this paper, we propose a unified structure and parallel algorithms to implement the FBMC. The FBMC system and parallel algorithms are constructed based on the normalized prototype filter. The coefficients of the normalized prototype filter can be pre-computed and stored. The proposed parallel algorithms have the same structure for various choices of time duration, subcarrier spacing and bandwidth. Combined with known parallel algorithms for the fast Fourier transform (FFT), the proposed algorithms fully parallelize the computations for the transmitter and receiver, which can run much faster than conventional serial algorithms as modern processors usually have massive parallel capability.
In the last two decades we observed a considerably improvement in algorithms' performances and their ability to solve hard combinatorial optimization problems. One of these problems is the knapsack sharing problem...
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ISBN:
(纸本)9781665442329
In the last two decades we observed a considerably improvement in algorithms' performances and their ability to solve hard combinatorial optimization problems. One of these problems is the knapsack sharing problem (KSP). The latter problem is a challenging variant of the well-known NP-hard single knapsack problem. In fact, we can find in the literature several exact and heuristic resolution approaches to solve the (KSP). We mainly propose here an improvement and an adaptation to parallel computing of one of the existing and most recent algorithm in the literature. The approach is a constructive tree search that runs in two phases: the initial solution construction phase and the second phase where we build the optimal solution through a customized branch and bound. We applied a parallel computing on this second phase in order to improve the overall computational time. Finally we present a comparative study on instances from literature to show the positive effect of parallel processing on the computing time.
Electromagnetic scattering from electrically large objects with multiscale features is an increasingly important problem in computational electromagnetics. A conventional approach is to use an integral equation-based ...
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Electromagnetic scattering from electrically large objects with multiscale features is an increasingly important problem in computational electromagnetics. A conventional approach is to use an integral equation-based solver that is then augmented with an accelerator, a popular choice being a parallel multilevel fast multipole algorithm (MLFMA). One consequence of multiscale features is locally dense discretization, which leads to low-frequency breakdown and requires nonuniform trees. To the authors' knowledge, the literature on parallel MLFMA for such multiscale distributions capable of arbitrary accuracy is sparse;this paper aims to fill this niche. We prescribe an algorithm that overcomes this bottleneck. We demonstrate the accuracy (with respect to analytical data) and performance of the algorithm for both PEC scatterers and point clouds as large as 755 lambda with several hundred million unknowns and nonuniform trees as deep as 16 levels.
This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice....
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Graph algorithms play a prominent role in several fields of sciences and engineering. Notable among them are graph traversal, finding the connected components of a graph, and computing shortest paths. There are severa...
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ISBN:
(纸本)9781479907298
Graph algorithms play a prominent role in several fields of sciences and engineering. Notable among them are graph traversal, finding the connected components of a graph, and computing shortest paths. There are several efficient implementations of the above problems on a variety of modern multiprocessor architectures. It can be noticed in recent times that the size of the graphs that correspond to real world data sets has been increasing. parallelism offers only a limited succor to this situation as current parallel architectures have severe short-comings when deployed for most graph algorithms. At the same time, these graphs are also getting very sparse in nature. This calls for particular work efficient solutions aimed at processing large, sparse graphs on modern parallel architectures. In this paper, we introduce graph pruning as a technique that aims to reduce the size of the graph. Certain elements of the graph can be pruned depending on the nature of the computation. Once a solution is obtained for the pruned graph, the solution is extended to the entire graph. We apply the above technique on three fundamental graph algorithms: breadth first search (BFS), Connected Components (CC), and All Pairs Shortest Paths (APSP). To validate our technique, we implement our algorithms on a heterogeneous platform consisting of a multicore CPU and a GPU. On this platform, we achieve an average of 35% improvement compared to state-of-the-art solutions. Such an improvement has the potential to speed up other applications that rely on these algorithms.
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