A Weighted Average Adaptive Cross Approximation

Jordon N. Blackburn, John C. Young, Robert J. Adams

Research output: Contribution to journalArticlepeer-review


The adaptive cross approximation (ACA) is considered for matrix structures where error control is lost. A weighted average form of the ACA is presented that mitigates the loss of error control. In the averaged ACA (AACA) algorithm, the ACA is applied to a matrix comprising linear combinations of the rows and columns of the original matrix. An efficient implementation of the weighted average algorithm is outlined. The performance of the ACA and AACA are examined for both static and time-harmonic integral equation solutions of problems for which loss of error control by the ACA is observed. The behaviors of the ACA and AACA are compared and discussed, and the AACA is observed to maintain error control for many matrices for which the ACA fails.

Original languageEnglish
Pages (from-to)8121-8129
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Issue number10
StatePublished - Oct 1 2023

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.


  • Adaptive cross approximation (ACA)
  • Schur complement
  • fast integral equation methods
  • low-rank matrix compression

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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