一种用于矩阵求逆的原位替换算法及硬件实现  

An in-situ substitution algorithm for matrix inversion and its hardware implementation

作　　者：张多利[1] 蒋雯 叶紫燕 宋宇鲲[1] 汪健[2] ZHANG Duoli;JIANG Wen;YE Ziyan;SONG Yukun;WANG Jian(School of Electronic Science and Applied Physics,Hefei University of Technology,Hefei 230601,China;No.214 Institute,China North Industries Group,Bengbu 233000,China)

机构地区：[1]合肥工业大学电子科学与应用物理学院,安徽合肥230601 [2]中国兵器工业集团第214研究所,安徽蚌埠233000

出　　处：《合肥工业大学学报（自然科学版）》2020年第1期75-80,共6页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(61106020)

摘　　要：对于数字信号处理、无线通信技术等数值计算领域中大量的矩阵求逆运算,采用传统的求逆算法,如伴随矩阵法、高斯消去法等,计算量庞大、过程复杂,且存储空间需求大、并行性低,硬件实现计算加速效率不高。文章提出一种原位替换矩阵求逆算法,针对算法设计地址控制和硬件架构,在Xilinx公司的Virtex7现场可编程逻辑门阵列(field programmable gate array,FPGA)中进行了硬件实现,验证了所设计的硬件架构在原存储空间内,能够并行高效地完成2^n阶单精度实数矩阵求逆运算,结果精度能达到10^-6。与基于Cholesky分解的矩阵求逆方法相比,该算法能取得近10倍的加速比;其并行性高,占用的存储和硬件资源少,具有较高的性能。In many numerical fields,such as digital signal processing,wireless communication technology and so on,there are a lot of matrix seeking inverse.The traditional inversion algorithm,such as adjoint matrix method,elementary transformation method,Gauss-Jordan elimination and so on,has huge computational complexity,complicated process,and has large storage space requirement and low parallelism,and the efficiency of hardware realization is not high.In this paper,based on the analysis of the characteristics of an inversion algorithm for in-situ substitution matrix,the hardware architecture of the algorithm is designed,which is implemented in the Virtex7 field programmable gate array(FPGA)of Xilinx company,and verifies that the hardware architecture is in the original storage space.It can achieve the inverse of 2^n order precision real matrix in parallel and efficiently,the result precision can reach 10^-6,and it can get nearly 10 times speedup compared with a matrix inversion method based on Cholesky decomposition.It has high parallelism,occupies less storage and hardware resources,and has high performance.

关 键 词：矩阵求逆 原位替换 硬件架构 并行计算 存储资源 

分 类 号：TN402[电子电信—微电子学与固体电子学]