Corrections to "Fast Multilevel Computation of Low-Rank Representation of mathcal {H} -Matrix Blocks'': Fast multilevel computation of low-rank representation of H-matrix blocks (IEEE Transactions on Antennas and Propagation (2016) 64:12 (5326-5334) DOI: 10.1109/TAP.2016.2617376)

Several asymptotic complexity expressions in [1] were overestimated and require correction. All the errors resulted from the same incorrect assumption: at the end of Section II, the computational complexity of calculating the singular value decomposition (SVD) of an m×n matrix A was presented as O(m2n+n3) —the cost of computing the full SVD A=UΣV† using the R-SVD algorithm [2] , assuming m≥n (otherwise m and n are interchanged). The algorithm in [1] , however, uses the SVD for computing Σ , V† , and only the first n columns of U , at an O(mn2+n3) cost only [2] . Indeed, the standard SVD implementations ensure that this computation costs O(mnmin[m,n]) [3] . Accordingly, [1] should have used SVD costs of {O(m2n),O(mn2)} rather than {O(n3),O(m2n)} , when {m<n,m≥n} . Using these impacts several complexity expressions in [1] and its conclusion as detailed next.