NDLI: Error Bound of the Multilevel Adaptive Cross Approximation (MLACA)

Content Provider	IEEE Xplore Digital Library
Author	Xinlei Chen Changqing Gu Heldring, A. Zhuo Li Qunsheng Cao
Copyright Year	1963
Abstract	An error bound of the multilevel adaptive cross approximation (MLACA), which is a multilevel version of the adaptive cross approximation-singular value decomposition (ACA-SVD), is rigorously derived. For compressing an off-diagonal submatrix of the method of moments (MoM) impedance matrix with a binary tree, the L-level MLACA includes L + 1 steps, and each step includes 2^L ACA-SVD decompositions. If the relative Frobenius norm error of the ACA-SVD used in the MLACA is smaller than ε, the rigorous proof in this communication shows that the relative Frobenius norm error of the L-level MLACA is smaller than (1 + ε)^L+1 - 1. In practical applications, the error bound of the MLACA can be approximated as ε(L + 1), because ε is always ≪1. The error upper bound can be used to control the accuracy of the MLACA. To ensure an error of the L-level MLACA smaller than ε for different L, the ACA-SVD threshold can be set to (1 + ε)^1/(L+1) - 1, which approximately equals ε/(L + 1) for practical applications.
Sponsorship	IEEE Antennas and Propagation Society
Starting Page	374
Ending Page	378
Page Count	5
File Size	271252
File Format	PDF
ISSN	0018926X
Volume Number	64
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2016-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Method of moments Approximation methods Impedance Signal processing algorithms Matrix decomposition Binary trees Upper bound multilevel adaptive cross approximation (MLACA) error bound method of moments (MoM) low- rank decomposition Error bound low-rank decomposition
Content Type	Text
Resource Type	Article
Subject	Condensed Matter Physics Electrical and Electronic Engineering

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