The randomly pivoted Cholesky algorithm (RPCholesky) computes a factorized rank‐ approximation of an positive‐semidefinite (psd) matrix. RPCholesky requires only entry evaluations and additional arithmetic operations, and it can be implemented with just a few lines of code. The method is particularly useful for approximating a kernel matrix. This paper offers a thorough new investigation of the empirical and theoretical behavior of this fundamental algorithm. For matrix approximation problems that arise in scientific machine learning, experiments show that RPCholesky matches or beats the performance of alternative algorithms. Moreover, RPCholesky provably returns low‐rank approximations that are nearly optimal. The simplicity, effectiveness, and robustness of RPCholesky strongly support its use in scientific computing and machine learning applications.

中文翻译：

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随机旋转的 Cholesky：具有很少入口评估的核矩阵的实际近似


随机旋转的 Cholesky 算法 （RPCholesky） 计算正半定 （psd） 矩阵的因分解秩近似。RPCholesky 只需要入场计算和额外的算术运算，并且只需几行代码即可实现。该方法对于近似核矩阵特别有用。本文对这种基本算法的经验和理论行为进行了全面的新研究。对于科学机器学习中出现的矩阵近似问题，实验表明 RPCholesky 的性能与替代算法相当或更好。此外，RPCholesky 可证明地返回几乎是最优的低秩近似值。RPCholesky 的简单性、有效性和稳健性有力地支持了它在科学计算和机器学习应用程序中的使用。