F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig Hybrid Cross Approximation of Integral Operators Hybrid Cross Approximation of Integral Operators

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A literature survey of low‐rank tensor approximation techniques (2013, neutral): “For an m × n matrix A , the so called cross approximation method [19, 34, 100, 248] produces an approximation of the form A (: , J ) A ( I, J ) − 1 A ( I,”
Black Box Low Tensor-Rank Approximation Using Fiber-Crosses (2009, methodology): “This effect is known for the matrix case [3] and can be circumvented by either a priori knowledge (positions of atoms) or by an additional random sampling (Algorithm 2) as follows: after finding a first preliminary pivot index by Algorithm 3 we also compute a second preliminary pivot index by Algori”
Hierarchical matrix techniques for low- and high-frequency Helmholtz problems (2007, background): “For the case f(l, j) = s(xl, yj), where s is an asymptotically smooth kernel, and xl and yj are restricted to two cluster that satisfy an admissibility condition, the ACA algorithm has been investigated theoretically in [7, 12].”
Likelihood approximation with hierarchical matrices for large spatial datasets (2017, methodology): “For this purpose, we propose using the Adaptive Cross Approximation (ACA) algorithm [23, 6, 11, 14, 13], which performs the approximations with a linear complexity O(n).”
Black box approximation of tensors in hierarchical Tucker format (2013, background): “From [2] it is well known that the pivot search can fail for matrices.”