Research on the Convergence of Iterative Method Using Mixed Precision Calculation Solving Complex Symmetric Linear Equation

Abstract

This article investigates the complex symmetric linear equations that appear in high-frequency electromagnetic-field analysis. As an efficient linear solver, we propose a mixed-precision iterative method with double- and double-double (DD)-precision floating-point numbers and an efficient implementation of DD-precision arithmetic with fused multiply-add instructions. Using the proposed method, we successfully reduce both iteration count and calculation time compared with the conventional method. Moreover, we demonstrate the relationship between multiple-precision arithmetic and the acceleration factor of the incomplete Cholesky factorization.