Matrix decomposition is a very important mathematical tool in numerical linear algebra for data processing. In this paper, we introduce a new randomized matrix decomposition algorithm, which is called randomized approximate SVD based on Qatar Riyal decomposition (RCSVD-QR). Our method utilize random sampling and the OR decomposition to address a serious bottlenck associated with classical SVD. RCSVD-QR gives satisfactory convergence speed as well as accuracy as compared to those state-of-the-art algorithms. In addition, we provides an estimate for the expected approximation error in Frobenius norm. Numerical experiments verify these claims.

翻译：矩阵分解是数值线性代数中用于数据处理的一个非常重要的数学工具。本文提出了一种新的随机矩阵分解算法，即基于QR分解的随机近似SVD（RCSVD-QR）。该方法利用随机采样和QR分解解决了经典SVD算法中的一个严重瓶颈问题。与现有最先进的算法相比，RCSVD-QR在收敛速度和精度方面均表现良好。此外，我们还给出了Frobenius范数下期望逼近误差的估计。数值实验验证了这些结论。