基于Jacobi算法对称矩阵特征值计算的FPGA实现

作者：袁生光，沈海斌 日期：2008-11-03/span> 浏览：3990 查看PDF文档

基于Jacobi算法对称矩阵特征值计算的FPGA实现

袁生光，沈海斌
（浙江大学 超大规模集成电路设计研究所，浙江 杭州 310027）

摘要：对称矩阵的特征值计算问题在数学和工程应用中都具有重要的实际意义，针对对称矩阵特征值计算这一问题提出了一种新的FPGA实现方案，并对该方案进行了验证和性能评估，最后，将它和目前已有的设计进行了速度与面积方面的对比。研究结果证实，该方案在速度不受影响的前提下，所占面积得到了减小。
关键词：对称矩阵；特征值计算；现场可编程门阵列；Jacobi算法；坐标施转数字计算机
中图分类号：TP273文献标识码：A文章编号：1001-4551(2008)10-0080-03

Implementation in FPGAs of eigenvalue calculation with Jacobi
algorithm for symmetric matrix
YUAN Sheng-guang, SHEN Hai-bin
（Institute of VLSI Design, Zhejiang University, Hangzhou 310027, China）
Abstract: Eigenvalue calculation for symmetric matrix is significant in mathematics and engineering. A novel architecture of FPGAs was demonstrated to solve eigenvalue calculation for symmetric matrix. Moreover, the performance of the architecture was validated and evaluated, and finally it was compared with others mentioned in some articles. The experimental results prove that the area of the implementation is less than others without reducing speed.
Key words: symmetric matrix; eigenvalue calculation; field-programmable gate array(FPGA); jacobi algorithm; coordinate rotation digital computer(CORDIC)
参考文献(References):
［1］BRAVO I, JIMENEZ P, MAZO M, et al. Implementation in FPGAs of Jacobi Method to Solve the Eigenvalue and Eigenvector Problem［C］//Field Programmable Logic and Applications, 2006. FPL’06. International Conference. Madrid:［s. n.］,2006:1-4.
［2］JOLLIFFE I T. Principal Component Analysis［M］. 2nd ed. New York: Springer Press,2002.
［3］张贤达.矩阵分析与应用［M］.北京:清华大学出版社,2004.
［4］BOUGANIS C, CHEUNG P, LEONG P H, et al. Hardware Efficient Architectures for Eigenvalue Computation［C］//Proceedings of the conference on Design, automation and test in Europe. Munich: European Design and Automation Association,2006:953-958.
［5］WILKINSON J H. The Algebraic Eigenvalue Problem［M］. London: Oxford Science Publications,1999.
［6］陈维新.线性代数［M］.北京:科学出版社，2000.
［7］GOTZE J, PAUL S, SAUER M. An efficient Jacobi-like algorithm for parallel eigenvalue computation［J］. IEEE Transactions on Computers,1993,42(9):1058-1065.
［8］王智霞,王广生.CORDIC算法在FPGA中的实现［J］.微处理机,2007,22(3):4-7.