Averaged adaptive cross approximation for structured matrices

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

doi:10.1109/ACES53325.2021.00049

Averaged adaptive cross approximation for structured matrices

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A modified form of the adaptive cross approximation (ACA) is considered for certain structured matrices for which the original ACA fails to provide controllably accurate matrix representations of low-rank submatrices. The modified ACA algorithm considered here is based on forming an averaged matrix, obtained via left- and right- multiplication of the original matrix block by sparse matrices that have LU factorizations. The performance of the modified ACA algorithm is examined for several sub-matrices for which the original ACA fails to provide controllably accurate representations, and significantly improved error control is observed.

Original language	English
Title of host publication	2021 International Applied Computational Electromagnetics Society Symposium, ACES 2021
ISBN (Electronic)	9781733509626
DOIs	https://doi.org/10.1109/ACES53325.2021.00049
State	Published - Aug 1 2021
Event	2021 International Applied Computational Electromagnetics Society Symposium, ACES 2021 - Virtual, Hamilton, Canada Duration: Aug 1 2021 → Aug 5 2021

Publication series

Name	2021 International Applied Computational Electromagnetics Society Symposium, ACES 2021

Conference

Conference	2021 International Applied Computational Electromagnetics Society Symposium, ACES 2021
Country/Territory	Canada
City	Virtual, Hamilton
Period	8/1/21 → 8/5/21

Bibliographical note

Publisher Copyright:
© 2021 Applied Computational Electromagnetics Society.

Funding

This work was supported in part by Office of Naval Research Grant N00014-16-1-3066. 978-1-7335096-2-6© 2021 ACES In (4), L and R are square matrices with nonzero elements on the main-diagonal and 2 shifted off-diagonals as defined below. To simplify the following discussion, it is assumed that M = N and N is even, in which case L = R. Extension to the cases where M ∕ N and/or M , N , or M and N are odd is straightforward.

Funders	Funder number
Office of Naval Research	N00014-16-1-3066

Keywords

Adaptive cross approximation (ACA)
Fast integral equation methods
Locally-corrected Nyström (LCN) method

ASJC Scopus subject areas

Computer Networks and Communications
Electrical and Electronic Engineering
Radiation

Access to Document

10.1109/ACES53325.2021.00049

Cite this

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title = "Averaged adaptive cross approximation for structured matrices",

abstract = "A modified form of the adaptive cross approximation (ACA) is considered for certain structured matrices for which the original ACA fails to provide controllably accurate matrix representations of low-rank submatrices. The modified ACA algorithm considered here is based on forming an averaged matrix, obtained via left- and right- multiplication of the original matrix block by sparse matrices that have LU factorizations. The performance of the modified ACA algorithm is examined for several sub-matrices for which the original ACA fails to provide controllably accurate representations, and significantly improved error control is observed.",

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doi = "10.1109/ACES53325.2021.00049",

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Blackburn, JN, Adams, RJ & Young, JC 2021, Averaged adaptive cross approximation for structured matrices. in 2021 International Applied Computational Electromagnetics Society Symposium, ACES 2021. 2021 International Applied Computational Electromagnetics Society Symposium, ACES 2021, 2021 International Applied Computational Electromagnetics Society Symposium, ACES 2021, Virtual, Hamilton, Canada, 8/1/21. https://doi.org/10.1109/ACES53325.2021.00049

Averaged adaptive cross approximation for structured matrices. / Blackburn, Jordon N.; Adams, Robert J.; Young, John C.
2021 International Applied Computational Electromagnetics Society Symposium, ACES 2021. 2021. (2021 International Applied Computational Electromagnetics Society Symposium, ACES 2021).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - A modified form of the adaptive cross approximation (ACA) is considered for certain structured matrices for which the original ACA fails to provide controllably accurate matrix representations of low-rank submatrices. The modified ACA algorithm considered here is based on forming an averaged matrix, obtained via left- and right- multiplication of the original matrix block by sparse matrices that have LU factorizations. The performance of the modified ACA algorithm is examined for several sub-matrices for which the original ACA fails to provide controllably accurate representations, and significantly improved error control is observed.

AB - A modified form of the adaptive cross approximation (ACA) is considered for certain structured matrices for which the original ACA fails to provide controllably accurate matrix representations of low-rank submatrices. The modified ACA algorithm considered here is based on forming an averaged matrix, obtained via left- and right- multiplication of the original matrix block by sparse matrices that have LU factorizations. The performance of the modified ACA algorithm is examined for several sub-matrices for which the original ACA fails to provide controllably accurate representations, and significantly improved error control is observed.

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KW - Fast integral equation methods

KW - Locally-corrected Nyström (LCN) method

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Averaged adaptive cross approximation for structured matrices

Abstract

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Conference

Bibliographical note

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Keywords

ASJC Scopus subject areas

Access to Document

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