Complexity Analysis of a Fast Directional Matrix-Vector Multiplication

Günther Of*, Raphael Watschinger

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


We consider a fast, data-sparse directional method to realize matrix-vector products related to point evaluations of the Helmholtz kernel. The method is based on a hierarchical partitioning of the point sets and the matrix. The considered directional multi-level approximation of the Helmholtz kernel can be applied even on high-frequency levels efficiently. We provide a detailed analysis of the almost linear asymptotic complexity of the presented method. Our numerical experiments are in good agreement with the provided theory.
Original languageEnglish
Title of host publicationHigh Performance Computing in Science and Engineering - 4th International Conference, HPCSE 2019, Revised Selected Papers
Subtitle of host publication4th International Conference, HPCSE 2019, Karolinka, Czech Republic, May 20–23, 2019, Revised Selected Papers
EditorsTomáš Kozubek, Peter Arbenz, Jiří Jaroš, Lubomír Říha, Jakub Šístek, Petr Tichý
PublisherSpringer, Cham
Number of pages21
ISBN (Electronic)978-3-030-67077-1
ISBN (Print)978-3-030-67076-4
Publication statusPublished - 2021
EventHPCSE 2019: High Performance Computing in Science and Engineering - Karolinka, Czech Republic
Duration: 20 May 201923 May 2019

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceHPCSE 2019
Country/TerritoryCzech Republic
Internet address


  • Helmholtz
  • Fast multipole method
  • Hierarchical matrix

ASJC Scopus subject areas

  • Numerical Analysis

Fields of Expertise

  • Information, Communication & Computing


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