2014/11/30 by David P. Woodruff · 4 citations
Computer Science · #cs.DS
paper · pdf · doi:10.1561/0400000060
published as Foundations and Trends in Theoretical Computer Science, Vol 10, Issue 1--2, 2014, pp 1--157 · fixed minor errors/typos in section 4.3, e.g., Fact 6 and its propagation, clarified when Lemma 4.2 can be applied, typos in section 4.2.3 (G should be applied on the left), other typos throughout
arxiv created 2015/02/10 · arxiv updated 2015/02/11
This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a (usually) random matrix with certain properties. Much of the expensive computation can then be performed on the smaller matrix, thereby accelerating the solution for the original problem. In this survey we consider least squares as well as robust regression problems, low rank approximation, and graph sparsification. We also discuss a number of variants of these problems. Finally, we discuss the limitations of sketching methods.