A Comparison of Sequential and GPU Implementations of Iterative Methods to Compute Reachability Probabilities

@inproceedings{CormieBowins2012ACO,
  title={A Comparison of Sequential and GPU Implementations of Iterative Methods to Compute Reachability Probabilities},
  author={Elise Cormie-Bowins},
  booktitle={GRAPHITE},
  year={2012}
}
We consider the problem of computing reachability probabilities: given a Markov chain, an initial state of the Markov chain, and a set of goal states of the Markov chain, what is the probability of reaching any of the goal states from the initial state? This problem can be reduced to solving a linear equation Ax = b for x, where A is a matrix and b is a vector. We consider two iterative methods to solve the linear equation: the Jacobi method and the biconjugate gradient stabilized (BiCGStab… 

Figures and Tables from this paper

Improving GPU Sparse Matrix-Vector Multiplication for Probabilistic Model Checking

Several methods to improve the run times of probabilistic model checking on general-purpose graphics processing units (GPUs) are presented and can bring a significant run time improvement - more than four times compared to the previous version of GPU-PRISM.

Performance Comparison of GPU-Based Jacobi Solvers Using CUDA Provided Synchronization Methods

Experiments have showed that Jacobi implementations based on the implemented Butterfly communication method have outperformed CUDA 10.0 provided critical execution methods like atomicAdd, atomicAdd_block and grid methods, respectively.

Parallelization of an Iterative Method for Solving Large and Sparse Linear Systems using the CUDA-Matlab Integration

This paper presents a parallel implementation of the Hybrid Bi-Conjugate Gradient Stabilized (BiCGStab(2)) iterative method in a Graphics Processing Unit (GPU) for solution of large and sparse linear

GPU-aided Model Checking of Markov Decision Processes

An implementation of the well known value iteration algorithm for probabilistic model checking of Markov decision processes in a parallel way on GPGPUs (general purpose graphics processor units) and an implementation for the CUDA (Compute Unified Device Architecture) interface are presented.

Parallel Implementation of the BiCGStab(2) Method in GPU Using CUDA and Matlab for Solution of Linear Systems

A parallel implementation of the Hybrid Bi-Conjugate Gradient Stabilized iterative method in Graphics Processing Unit (GPU) for solution of large and sparse linear systems and shows that the exploitation of parallelism by using this new technology can provide a significant computational performance.

PROGRAMAÇÃO PARALELA DE UM MÉTODO ITERATIVO PARA SOLUÇÃO DE GRANDES SISTEMAS DE EQUAÇÕES LINEARES USANDO A INTEGRAÇÃO CUDA-MATLAB

A parallel implementation of the BiCGStab method for solving large linear systems using a Graphics Processing Unit through the CUDA-Matlab integration, in which the method operations are performed in the processing cores of the GPU by the Matlab built-in functions to provide a high computational performance.

Efficient implementation of Jacobi iterative method for large sparse linear systems on graphic processing units

The proposed algorithm helps to optimize the parallel implementation on GPU and the performance analysis of GPU-based (using CUDA) algorithm of the implementation of this algorithm is compared to the corresponding serial CPU-based algorithm.

Acceleration of Computational Fluid Dynamics Analysis by using Multiple GPUs

A scheme to improve the performance of CFD applications based on multi-GPUs by changing the matrix multiplication method from scalarbased scheme to enhanced vector-based scheme and using direct memory access (DMA) scheme among multiGPUs to reduce the latency.

References

SHOWING 1-10 OF 15 REFERENCES

Parallel Iterative Linear Solvers on GPU: A Financial Engineering Case

  • A. GaikwadI. Toke
  • Computer Science
    2010 18th Euromicro Conference on Parallel, Distributed and Network-based Processing
  • 2010
This paper focuses on the design of Krylov subspace based iterative solvers to take advantage of massive parallelism of general purpose Graphics Processing Units (GPU)s and discusses data structures and efficient implementation of these solvers on the NVIDIA's CUDA platform.

Parallel probabilistic model checking on general purpose graphics processors

Algorithms for parallel probabilistic model checking on general purpose graphic processing units (GPGPUs) with significant speedup over the standard CPU implementation of the tool are presented.

Efficient Probabilistic Model Checking on General Purpose Graphics Processors

Algorithms for parallel probabilistic model checking on general purpose graphic processing units (GPGPUs) based on matrix vector multiplication that can achieve considerable runtime improvements compared to their counterparts on standard architectures are presented.

Incremental quantitative verification for Markov decision processes

Efficient incremental techniques for quantitative verification of Markov decision processes are presented, which are able to re-use results from previous verification runs, based on a decomposition of the model into its strongly connected components (SCCs).

Principles of model checking

Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field.

Programming Massively Parallel Processors. A Hands-on Approach

  • Jie Cheng
  • Computer Science
    Scalable Comput. Pract. Exp.
  • 2010
This comprehensive test/reference provides a foundation for the understanding and implementation of parallel programming skills which are needed to achieve breakthrough results by developing parallel applications that perform well on certain classes of Graphic Processor Units (GPUs).

Structured analysis techniques for large Markov chains

An overview of analysis techniques based on model structure is given and the availability of these new techniques are described and future research directions in the field are outlined.

CUDA Accelerated LTL Model Checking

This paper redesigns the maximal accepting predecessors algorithm in terms of matrix-vector product in order to accelerate LTL model checking on many-core GPU platforms and demonstrates that using the NVIDIA CUDA technology results in a significant speedup of verification process.

Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems

Numerical experiments indicate that the new variant of Bi-CG, named Bi- CGSTAB, is often much more efficient than CG-S, so that in some cases rounding errors can even result in severe cancellation effects in the solution.

Templates for the solution of linear systems: building blocks for iterative methods

  • R. Barrett
  • Computer Science
    Software, environments, tools
  • 1994
In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the