Randomly pivoted Cholesky (RPCholesky) is an algorithm for constructing a low-rank approximation of a positive-semidefinite matrix using a small number of columns. This paper develops an accelerated version of RPCholesky that employs block matrix computations and rejection sampling to efficiently simulate the execution of the original algorithm. For the task of approximating a kernel matrix, the accelerated algorithm can run over $40\times$ faster. The paper contains implementation details, theoretical guarantees, experiments on benchmark data sets, and an application to computational chemistry.

翻译：随机主元Cholesky分解（RPCholesky）是一种利用少量列构造半正定矩阵低秩近似的算法。本文开发了RPCholesky的加速版本，该版本采用分块矩阵计算和拒绝采样技术来高效模拟原始算法的执行过程。对于核矩阵近似任务，加速算法的运行速度可提升超过$40$倍。本文包含实现细节、理论保证、基准数据集实验以及计算化学领域的应用案例。