Computing and Visualization in Science

, Volume 20, Issue 3–6, pp 71–84 | Cite as

Hierarchical matrix arithmetic with accumulated updates

  • Steffen BörmEmail author
Special Issue CS Symposium 2016


Hierarchical matrices can be used to construct efficient preconditioners for partial differential and integral equations by taking advantage of low-rank structures in triangular factorizations and inverses of the corresponding stiffness matrices. The setup phase of these preconditioners relies heavily on low-rank updates that are responsible for a large part of the algorithm’s total run-time, particularly for matrices resulting from three-dimensional problems. This article presents a new algorithm that significantly reduces the number of low-rank updates and can shorten the setup time by 50% or more.



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsChristian-Albrechts-Universität zu KielKielGermany

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