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

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 doubledouble (DD)-precision floating-point numbers and an efficient implementation of DD-precision arithmetic with fused multiplyadd 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.