Revisiting the Adjoint Matrix for FPGA Calculating the Triangular Matrix Inversion

Abstract

Due to the robustness, the matrix inversion methods based on matrix factorization are often adopted in engineering while the triangular matrix inversion is one key part of those methods. This brief reviews the adjoint matrix and presents a novel scheme for field-programmable gate arrays (FPGAs) calculating the triangular matrix inversion. Employing the more characteristics of both the triangular matrix and its inversion, the proposed diagonal-wise algorithm for the triangular matrix inversion has the high parallelism and extensibility in the hardware implementation and is suitable for the different matrix triangular factorization (QR, LDL, Cholesky and LU). Meanwhile, the recursive diagonal-wise algorithm is designed for the large scale triangular matrices. Compared with the traditional row-/column-wise methods, our algorithm has a good performance at the low computation load. Finally, the experiments are conducted on one Xilinx Virtex-7 FPGA to illustrate the performances of the four different methods.