Strong rank revealing LU factorizations

By L. Miranian, Ming Gu. 2003

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Sketching as a Tool for Numerical Linear Algebra (2014, background): “decomposition deterministic. We will see that this is possible as well, as shown in [21]. Finally, there are several interesting results on CUR developed within the numerical linear algebra community [118, 119, 55, 54, 61, 101, 95, 56, 15, 112]. For example, [118, 119, 55, 54] discuss the so-called ”
Fast Direct Methods for Gaussian Processes (2014, background): “ computing fast low-rank decompositions. These include techniques like pseudo-skeletal approximations [23], interpolatory decomposition [17], randomized algorithms [19], [36], [52], rank-revealing LU [39], [42], adaptive cross approximation [44] (ACA) (which is a minor variant of partial pivoted LU)”
Numerical Linear Algebra (2011, background): “…Linear Algebra 5 Lji = Aji − ∑i−1 k=1 LjkUki end for j = i + 1 to n Uij = ( Aij − ∑i−1 k=1 LikUkj ) /Lii end end Finally, note that there are also generalizations of LU to non-square and singular matrices, such as rank revealing LU factorization; see Pan (2000) and Miranian and Gu (2003).”