2024/08/23 by Quinlan, James, Omtzigt, E. Theodore L.
#65F05 (Primary) 65F50 (Secondary) #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2408.13400
This research investigates using a mixed-precision iterative refinement method using posit numbers instead of the standard IEEE floating-point format. The method is applied to solve a general linear system represented by the equation Ax = b, where A is a large sparse matrix. Various scaling techniques, such as row and column equilibration, map the matrix entries to higher-density regions of machine numbers before performing the O(n3) factorization operation. Low-precision LU factorization followed by forward/backward substitution provides an initial estimate. The results demonstrate that a 16-bit posit configuration combined with equilibration produces accuracy comparable to IEEE half-precision (fp16), indicating a potential for achieving a balance between efficiency and accuracy.