This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-specified rank. The algorithms are simple, accurate, numerically stable, and provably correct. Moreover, each method is accompanied by an informative error bound that allows users to select parameters a priori to achieve a given approximation quality. These claims are supported by numerical experiments with real and synthetic data.

翻译：本文描述一组用于从矩阵随机线性图像(称为草图)中构建输入矩阵的低端近似值的算法。 这些方法可以保存输入矩阵的结构属性, 如正正模无限性, 并且可以用用户指定的级别产生近近似值。 这些算法简单、 准确、 数字稳定, 并且可以准确。 此外, 每种方法都伴随着一个信息错误, 用户可以选择一个前置参数来达到给定的近近似质量。 这些索赔都得到了用真实和合成数据进行的数字实验的支持 。