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.

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