In this paper we investigate the use of half-precision Kronecker product singular value decomposition (SVD) approximations as preconditioners for large-scale Tikhonov regularized least squares problems. Half precision reduces storage requirements and has the potential to greatly speedup computations on certain GPU architectures. We consider both standard PCG and flexible PCG algorithms, and investigate, through numerical experiments on image deblurring problems, the trade-offs between potentially faster convergence with the additional cost per iteration when using this preconditioning approach. Moreover, we also investigate the use of several regularization parameter choice methods, including generalized cross validation and the discrepancy principle.

翻译：本文研究了利用半精度Kronecker积奇异值分解（SVD）近似作为大规模Tikhonov正则化最小二乘问题预条件子的方法。半精度可降低存储需求，并有望在特定GPU架构上显著加速计算。我们同时考虑了标准PCG算法与柔性PCG算法，并通过图像去模糊问题的数值实验，探究了采用该预条件方法时潜在更快收敛速度与每迭代步额外计算成本之间的权衡。此外，本文还研究了多种正则化参数选择方法，包括广义交叉验证和偏差原理。