May 18 – 22, 2026
Virginia Tech
America/New_York timezone

Mixed Precision General Alternating-Direction Implicit Method for Solving Large Sparse Linear Systems

May 18, 2026, 11:25 AM
25m
Torgersen Hall 3100

Torgersen Hall 3100

Minisymposium Talk Approximate Computing in Numerical Linear Algebra Approximate Computing in Numerical Linear Algebra

Speaker

Juan Zhang

Description

Our work presents a novel mixed precision formulation of the General Alternating-Direction Implicit (GADI) method, designed to accelerate the solution of large-scale sparse linear systems $Ax=b$. By solving the computationally intensive subsystems in low precision (e.g., Bfloat16 or FP32) and performing residual and solution updates in high precision, the proposed method significantly reduces execution time without compromising the final solution accuracy. We provide a comprehensive rounding error analysis that establishes convergence rates and limiting accuracies under mixed precision arithmetic. Additionally, we introduce a robust strategy based on Gaussian Process Regression (GPR) for selecting the optimal regularization parameter $\alpha$. Performance benchmarks on an NVIDIA A100 GPU demonstrate that mixed precision GADI achieves speedups of up to 3.1× compared to standard double precision implementations on large-scale convection-diffusion and reaction-diffusion problems.

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