Fixed-point arithmetic error analysis of sparse LU decomposition on FPGAs

Abstract

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.