The generalized singular value decomposition (GSVD) is a powerful tool for solving discrete ill-posed problems. In this paper, we propose a two-sided uniformly randomized GSVD algorithm for solving the large-scale discrete ill-posed problem with the general Tikhonov regularization. Based on two-sided uniform random sampling, the proposed algorithm can improve the efficiency with less computing time and memory requirement and obtain expected accuracy. The error analysis for the proposed algorithm is also derived. Finally, we report some numerical examples to illustrate the efficiency of the proposed algorithm.

翻译：广义奇异值分解（GSVD）是求解离散不适定问题的有力工具。本文针对一般Tikhonov正则化的大规模离散不适定问题，提出了一种双侧均匀随机化GSVD算法。该算法基于双侧均匀随机采样，能以更少的计算时间和内存需求提高计算效率，并获得预期精度。文中同时推导了所提算法的误差分析。最后，我们通过数值算例验证了该算法的有效性。