Fixed-point arithmetic error analysis of sparse LU decomposition on FPGAs
Mohammad Saeed Feali, Arash Ahmadi, Abdosamad Hamidi, Majid Ahmadi · 2017
FPGAs are becoming an attractive platform for accelerating many computations including scientific applications. These applications demand high performance and high precision arithmetic. Decomposition of a matrix into lower and upper triangular matrices (LU decomposition) is a vital part of many scientific and engineering applications. This paper evaluates the accuracy of a fixed-point LU decomposition based on FPGA. Fixed-point architecture of LU decomposition is implemented on FPGA. Then several matrices with different sizes and random elements are decomposed using this architecture by various word-lengths. Using random matrices and different word-lengths, descriptive analysis of error is performed.