一种实对称矩阵特征值快速求解方法研究  

Research on a fast method for solving eigenvalues of real symmetric matrix

作　　者：彭永健 廖晓慧 张鹏飞 Peng Yongjian;Liao Xiaohui;Zhang Pengfei(The 29 th Research Institute of China Electronics Technology Group Corporation,Chengdu 610029,China)

机构地区：[1]中国电子科技集团公司第二十九研究所,四川成都610036

出　　处：《无线互联科技》2023年第2期112-114,共3页Wireless Internet Technology

摘　　要：实对称矩阵特征分解在工程项目中经常遇到需要快速求解特征值和特征向量,文章提出了一种基于FPGA的高效并行实对称矩阵特征值分解方法。通过构造旋转矩阵一次消除矩阵多个元素,让矩阵快速收敛为对角阵,从而得到原实对称矩阵的特征值和特征向量。并根据工程误差需求通过Matlab仿真确定了算法循环次数,在FPGA上验证了算法的可行性和快速性。Eigendecomposition of real symmetric matrices is often encountered in engineering projects,and it is necessary to quickly solve eigenvalues and eigenvectors.This paper proposes an efficient parallel real symmetric matrix eigenvalue decomposition method based on FPGA.By constructing a rotation matrix to eliminate multiple elements of the matrix at one time,the matrix can quickly converge to a diagonal matrix,and the eigenvalues and eigenvectors of the original real symmetric matrix can be obtained.According to the engineering error requirements,the cycle times of the algorithm are determined by Matlab simulation,and the feasibility and rapidity of the algorithm are verified on FPGA.

关 键 词：实对称矩阵 特征值分解 快速收敛 旋转矩阵 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]