Iterative Algorithms on Heterogeneous Network Computing: Parallel Polynomial Root Extracting

This paper deals with the numerical solution of financial applications, more specifically the computation of American and European options derivatives modeled by boundary value problems. In such applications we have to solve large-scale algebraic linear systems. We concentrate on synchronous and asynchronous parallel iterative algorithms carried out on Grid’5000, by using an experimental peer-to-peer platform. The properties of the operators arising in the discretized problem ensure the convergence of the parallel iterative synchronous and asynchronous algorithms. Different detection convergence algorithms are tested for asynchronous iterations. Computational experiments performed on distributed architectures are presented and analyzed.

In this paper, we investigate the performance of Parallel Discrete Event Simulation (PDES) on a cluster of many-core Intel KNL processors. Specifically, we analyze the impact of different Global Virtual Time (GVT) algorithms in this environment and contribute three significant results. First, we show that it is essential to isolate the thread performing MPI communications from the task of processing simulation events, otherwise the simulation is significantly imbalanced and performs poorly. This applies to both synchronous and asynchronous GVT algorithms. Second, we demonstrate that synchronous GVT algorithm based on barrier synchronization is a better choice for communication-dominated models, while asynchronous GVT based on Mattern's algorithm performs better for computation-dominated scenarios. Third, we propose Controlled Asynchronous GVT (CA-GVT) algorithm that selectively adds synchronization to Mattern-style GVT based on simulation conditions. We demonstrate that CA-GVT outperforms both barrier and Mattern's GVT and achieves about 8% performance improvement on mixed computation-communication models. This is a reasonable improvement for a simple modification to a GVT algorithm.

Distributed computing over large networks often suffers poor performances due to architecture heterogeneity and synchronization delays. This is the case of classical computing libraries which are dedicated to parallel machines or clusters. To achieve a better efficiency on multisites heterogeneous networks, one can use asynchronous algorithms which are less sensible to communication delays and loss of messages. Implementing such algorithms with classical MPI versions is not the best choice. We propose Jace, a Java environment dedicated to distributed asynchronous computations, and more especially to asynchronous iterations-asynchronous communications algorithms. It contains all facilities to build a parallel virtual machine and to implement computing tasks in a message passing style. Communications have a special semantic adapted to asynchronism. First tests on a simple Jacobi algorithm clearly show the benefits of our environment to compute on a multisite heterogeneous network, that is, the grid.

Construction of an ontological metamodel of iterative algorithms is proposed to structure knowledge about these algorithms and their implementation. The metamodel will automate the design and use of specialized software for solving specific applied modeling problems. The advantage of iterative GMDH algorithms over combinatorial ones is that they allow the big datasets processing. The known generalized iterative algorithm, allows you to create typical architectures of previously developed modifications of these algorithms when setting up various modes of operation of this algorithm. The authors have developed an ontological metamodel of iterative GMDH algorithms using the Protégé environment.

article Free Access Share on Software support for heterogeneous computing Authors: Howard Jay Siegel Purdue University, West Lafayette, Indiana Purdue University, West Lafayette, IndianaView Profile , Henry G. Dietz Purdue University, West Lafayette, Indiana Purdue University, West Lafayette, IndianaView Profile , John K. Antonio Texas Tech University, Lubbock Texas Tech University, LubbockView Profile Authors Info & Claims ACM Computing SurveysVolume 28Issue 1March 1996 pp 237–239https://doi.org/10.1145/234313.234411Published:01 March 1996Publication History 21citation711DownloadsMetricsTotal Citations21Total Downloads711Last 12 Months67Last 6 weeks17 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

This paper describes a methodology for the implementation of asynchronous parallel iterative algorithms, which is the domain decomposition method. This approach reduces the cost of synchronization that affects synchronous algorithms. As an application of the proposed approach, the algorithms based on the well-known point-SOR methods are presented in both synchronous and asynchronous forms. Results obtained using the MIMD (Multiple Instruction stream Multiple data stream) superparallel computer are given, for the model problem of the solution of a Poisson equation.

Transmitted wavefront testing of window glass with confocal photon-sieves radial-shearing interferometry based on deep learning

This paper considers the non-cooperative maximization of mutual information in the vector Gaussian interference channel in a fully distributed fashion via game theory. This problem has been widely studied in a number of works during the past decade for frequency-selective channels, and recently for the more general MIMO case, for which the state-of-the art results are valid only for nonsingular square channel matrices. Surprisingly, these results do not hold true when the channel matrices are rectangular and/or rank deficient matrices. The goal of this paper is to provide a complete characterization of the MIMO game for arbitrary channel matrices, in terms of conditions guaranteeing both the uniqueness of the Nash equilibrium and the convergence of asynchronous distributed iterative waterfilling algorithms. Our analysis hinges on new technical intermediate results, such as a new expression for the MIMO waterfilling projection valid (also) for singular matrices, a mean-value theorem for complex matrix-valued functions, and a general contraction theorem for the multiuser MIMO watefilling mapping valid for arbitrary channel matrices. The quite surprising result is that uniqueness/convergence conditions in the case of tall (possibly singular) channel matrices are more restrictive than those required in the case of (full rank) fat channel matrices. We also propose a modified game and algorithm with milder conditions for the uniqueness of the equilibrium and convergence, and virtually the same performance (in terms of Nash equilibria) of the original game.

This article is concerned with the asynchronous $H_{\infty }$ control design based on model-free policy iteration (PI) algorithm for a class of discrete-time hidden Markov jump system, where a hidden Markov model is developed to characterize the asynchronous phenomenon between the controller modes and the system modes. A pair of zero-sum asynchronous control and disturbance strategies are constructed to achieve a tradeoff between value function and control performance. The presented approach shows two pivotal aspects: 1) the asynchronous PI algorithm is not dependent on strict temporal alignment between the controller and the system's dynamics, enhancing flexibility of the control scheme and 2) it relies on the collected data to solve the algebraic Reccati equation iteratively, which avoids the need for system-internal and transfer probability information, and circumvents the interference of coupled terms. Subsequently, it is verified that the designed PI algorithm monotonically converges to an optimal solution and the system based on this optimal solution is stochastically stable in the mean-square sense. Finally, the effectiveness of this approach is validated by conducting a simulation experiment on a DC motor device system.

We present a game-theoretic treatment of distributed power control in CDMA wireless systems using outage probabilities. We first prove that the noncooperative power control game considered admits a unique Nash equilibrium (NE) for uniformly strictly convex pricing functions and under some technical assumptions on the SIR threshold levels. We then analyze global convergence of continuous-time as well as discrete-time synchronous and asynchronous iterative power update algorithms to the unique NE of the game. Furthermore, we show that a stochastic version of the discrete-time update scheme, which models the uncertainty due to quantization and estimation errors, converges almost surely to the unique NE point. We finally investigate and demonstrate the convergence and robustness properties of these update schemes through simulation studies.

Defining tasks as independent entities with identical execution time and workload as the number of tasks, the author proposes a partially asynchronous and iterative algorithm for distributed load balancing, shows its properties, and reports its simulation results. The algorithm converges geometrically according to a theorem proved elsewhere. He proves that the algorithm can achieve the maximum load imbalance of not more than (/sup d///sub 2/) tasks, where d is the diameter of a network. His simulation of a synchronous version of the algorithm not only validated the properties but also showed that the algorithm could produce much smaller load imbalances for hypercubes. The obtained imbalances for hypercubes of order up to ten were no more than two tasks and 56% of the sample runs produced only one task difference, as opposed to the theoretical maximum of six tasks. >

Graphics Processing Units (GPUs) have proven to be highly effective at accelerating processing speed for a large range of scientific and general purpose applications. As data needs increase, and more complex data analysis methods are used, the processing requirements for solving scientific problems also correspondingly increase. The massive parallel processing power of GPUs can be harnessed and used alongside multi-core CPUs to address these increased needs and allow acceleration of scientific algorithms to open up new realms of possibilities. As an example, there are many scientific problems that require solving non-linear optimization problems of multiple variables across large arrays of data. These types of problems are classified as highly difficult and require a great deal of computational time to solve using traditional techniques. By utilizing modern local optimization techniques, such as the iterative quasi-Newton algorithms, and combining them with the computational throughput of a CPU-GPU heterogeneous computing platform, we can greatly decrease the processing time required to solve scientific problems of this form.

Shared-memory multiprocessors commonly use shared variables for synchronization. Our simulations of real parallel applications show that large-scale cache-coherent multiprocessors suffer significant amounts of invalidation traffic due to synchronization. Large multiprocessors that do not cache synchronization variables are often more severely impacted. If this synchronization traffic is not reduced or managed adequately, synchronization references can cause severe congestion in the network. We propose a class of adaptive back-off methods that do not use any extra hardware and can significantly reduce the memory traffic to synchronization variables. These methods use synchronization state to reduce polling of synchronization variables. Our simulations show that when the number of processors participating in a barrier synchronization is small compared to the time of arrival of the processors, reductions of 20 percent to over 95 percent in synchronization traffic can be achieved at no extra cost. In other situations adaptive backoff techniques result in a tradeoff between reduced network accesses and increased processor idle time.

Asynchronous grid computation for American options derivatives

In this paper we are interested in studying the development of parallel algorithms to solve nonlinear wave equations. Both synchronous and asynchronous algorithms contexts are considered. The solver is based on the multisplitting Newton method that provides a coarse-grained scheme. Experiments are carried out in both homogeneous and heterogeneous grid environments. According to the configuration environment, the behaviors of parallel synchronous and asynchronous algorithms are analyzed. Experiments allow us to draw some conclusions about the use of parallel iterative algorithms in grid computing environment.