# 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…

## 15 Citations

### Improving GPU Sparse Matrix-Vector Multiplication for Probabilistic Model Checking

- Computer ScienceSPIN
- 2012

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

- Computer ScienceIEEE Access
- 2020

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

- Computer Science
- 2014

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

- Computer Science
- 2014

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

- Computer Science
- 2014

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

- Computer Science, Mathematics
- 2014

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.

### A high-throughput hybrid task and data parallel Poisson solver for large-scale simulations of incompressible turbulent flows on distributed GPUs

- Computer ScienceJ. Comput. Phys.
- 2021

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

- Computer ScienceThe Journal of Supercomputing
- 2016

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.

### Analysis of the convergence properties for a non-linear implicit Equilibrium Flux Method using Quasi Newton-Raphson and BiCGStab techniques

- MathematicsComput. Math. Appl.
- 2016

### Acceleration of Computational Fluid Dynamics Analysis by using Multiple GPUs

- Computer Science
- 2016

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.

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