We propose superfast (aka sublinear cost) algorithms for two fundamental problems of Matrix Computations, that is, Norm Estimation and Iterative Refinement of Low Rank Approximation (LRA). A superfast algorithm only accesses a small fraction of all entries of an input matrix and cannot accurately estimate their norms or output their close LRA for worst case inputs. Thus, we begin with some well-known algorithms solving these problems in linear or super linear time and then propose superfast modifications, which still promise to succeed for most or a large class of inputs, according to our tests with real world inputs.

翻译：我们针对矩阵计算的两个基本问题——范数估计与低秩逼近的迭代精化，提出了超快速（即次线性代价）算法。超快速算法仅访问输入矩阵所有条目中的一小部分，因此无法对最坏情况输入准确估计其范数或输出其精确低秩逼近。为此，我们从一些已知的线性或超线性时间求解这些问题的算法出发，提出超快速改进版本。根据我们在真实世界输入上的测试，这些改进算法仍能对大多数或广泛类别的输入保证成功。