毕业设计论文 高斯消去法求解线性方程组.doc

PAGE  摘 要 高斯消去法是求解线性方程组的最基本的方法之一。为了充分利用GPU (Graphics Processing Unit，图形处理器)的并行处理能力，本文改进了高斯列主元消去法的实现过程，从而提高了求解线性方程组的速度。并研究了在不同方程组阶数下，GPU对这此算法的加速效果。NVIDIA新近推出的GPU计算平台采用矩阵型的计算架构，对处理大型矩阵具有极大的优势，且相对CPU有着更高的算法可并行性和计算效率。本文力图基于GPU的CUDA开发环境，利用GP-GPU的计算特性实现求解线性方程组，以提高算法的运行效率。最后，本文用C语言实现了高斯列主元消去算法求解线性方程组的基本过程，并分别在NVIDIA GPU并行计算平台和Intel CPU计算平台上加以运行，同时进行了两种计算平台上算法实现的性能比较。 关键词：求解线性方程组；高斯消去法；GPU；CUDA；并行计算 Abstract Gaussian elimination method is one of the most basic methods for solving linear equations. In order to take full advantage of GPU (Graphics Processing Unit, GPU) of the parallel processing capability, this paper improved Gaussian PCA out of the realization of the process of elimination, resulting in improved system of linear equations to solve the speed. And studied the different equations in a few bands, GPU accelerated the effect of this algorithm. NVIDIA recently introduced the use of GPU computing platform for the calculation of matrix-type structure, to deal with large-scale matrix has great advantages, and the relative CPU algorithm has higher computational efficiency and parallelism. This article seeks to CUDA for GPU-based development environment, the use of GP-GPU computing features to achieve the solution of linear equations in order to improve the efficiency of algorithm. Finally, using C language realization of the Gaussian elimination algorithm PCA out of linear equations to solve the basic process and NVIDIA GPU in parallel computing platform and Intel CPU computing platform to be run, at the same time on two types of computing platforms algorithm Performance Comparison of the achievement. Key?words: Solving?linear?equations;?Gaussian?elimination?method; GPU; CUDA; Parallel?Computing 目 录  TOC \o 1-3 \h \z \u  HYPERLINK \l _Toc231887905 第一章 绪论  PAGEREF _Toc231887905 \h 1  HYPERLINK \l _Toc231887906 1.1 引言  PAGEREF _Toc231887906 \h 1  HYPERLINK \l _Toc231887907 1.2 论文研究背景  PAGEREF _Toc231887907 \h 1  HYPERLINK \l _Toc231887908 1