This talk introduces a novel mixed-precision formulation of the general alternating-direction implicit (GADI) method, specifically designed to accelerate the solution of large-scale sparse linear systems. By computing the computationally intensive subsystems in low precision (e.g., Bfloat16 or FP32) while performing residual calculations and solution updates in high precision, the proposed approach achieves a significant reduction in execution time without sacrificing the final solution accuracy. We present a comprehensive rounding error analysis, which rigorously establishes the convergence rate and limiting accuracy of the method under mixed-precision arithmetic. Furthermore, we propose a robust strategy based on Gaussian process regression (GPR) for the optimal selection of the regularization parameter. Performance benchmarks conducted on an NVIDIA A100 GPU demonstrate that the mixed-precision GADI method delivers speedups of up to 2.6× compared to standard double-precision implementations, with tests performed on large-scale convection-diffusion and reaction-diffusion problems.