TY - JOUR

T1 - Corrections to "Fast Multilevel Computation of Low-Rank Representation of mathcal {H} -Matrix Blocks''

T2 - 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)

AU - Brick, Yaniv

AU - Yilmaz, Ali E.

N1 - Publisher Copyright: © 2017 IEEE.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85021752976&partnerID=8YFLogxK

U2 - https://doi.org/10.1109/TAP.2017.2697413

DO - https://doi.org/10.1109/TAP.2017.2697413

M3 - مقالة

SN - 0018-926X

VL - 65

SP - 3315

EP - 3315

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

IS - 6

M1 - 7938531

ER -