任意阶矩阵求逆的算法优化和硬件实现

Optimization of arbitrary order matrix inversion algorithm and its implementation on FPGA

文章在深入研究原位替换算法的基础上,提出一种新的大维度矩阵求逆算法。该算法通过主元交换和行修正操作,将算法应用范围扩展至非奇异矩阵。与使用二次约化处理的算法相比,该文算法运算量约为前者的60%。综合考虑运算速度、硬件资源及文中新算法的高并行性,分别在TSMC 28 nm工艺和Xilinx XC7V2000T芯片上完成硬件实现,并在现场可编程门阵列(field programmable gate array,FPGA)上进行了功能和性能验证。硬件实测结果表明,文中设计可在339 572个周期内完成128阶非奇异单精度浮点矩阵求逆任务,结果精度达10-5。与基于高斯消元法的大规模矩阵求逆实现相比,文中硬件实现时存储资源大约节省了46%。

On the basis of the study of the in-situ replacement algorithm,a new inverse algorithm for large-scale matrix is proposed.It can be used to compute nonsingular matrix by means of diagonal element exchange and row correction.Compared with the algorithm of the second reduction,the computation amount of the proposed algorithm is about 60%of the former.In consideration of the high parallelism of the computing speed,hardware resources and the algorithm,the hardware implementation of the TSMC 28 nm process and Xilinx XC7V2000T chip was completed,and the function and performance verification on the field programmable gate array(FPGA)was conducted.The results show that this design can compute the inverse of 128-order single precision floating-point nonsingular matrix in 339 572 cycles,and the precision can reach 10-5.Compared with the large-scale matrix inversion based on Gauss-Jordan elimination,the proposed algorithm saves about 46%of the storage resources in hardware design.