research-article

Complex Root Finding Algorithm Based on Delaunay Triangulation

Author:

Piotr KowalczykAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 41, Issue 3

Article No.: 19, Pages 1 - 13

https://doi.org/10.1145/2699457

Published: 01 June 2015 Publication History

Abstract

A simple and flexible algorithm for finding zeros of a complex function is presented. An arbitrary-shaped search region can be considered and a very wide class of functions can be analyzed, including those containing singular points or even branch cuts. The proposed technique is based on sampling the function at nodes of a regular or a self-adaptive mesh and on the analysis of the function sign changes. As a result, a set of candidate points is created, where the signs of the real and imaginary parts of the function change simultaneously. To verify and refine the results, an iterative algorithm is applied. The validity of the presented technique is supported by the results obtained in numerical tests involving three different types of functions.

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Cited By

Liu XTang DLiu X(2025)An enhanced argument principle algorithm for exact complex transcendental eigenvalue analysis of damped structuresJournal of Sound and Vibration10.1016/j.jsv.2024.118751595(118751)Online publication date: Jan-2025
https://doi.org/10.1016/j.jsv.2024.118751
Trofimowicz DStefański TPietruszka PGulgowski J(2024)Testing Stability of FDTD in Media Described by Time-Fractional Constitutive Relations2024 25th International Microwave and Radar Conference (MIKON)10.23919/MIKON60251.2024.10633996(137-142)Online publication date: 1-Jul-2024
https://doi.org/10.23919/MIKON60251.2024.10633996
Pelloni BSmith D(2024)Revivals, or the Talbot effect, for the Airy equationStudies in Applied Mathematics10.1111/sapm.12699153:2Online publication date: 30-Apr-2024
https://doi.org/10.1111/sapm.12699
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Index Terms

Complex Root Finding Algorithm Based on Delaunay Triangulation
1. Mathematics of computing
  1. Mathematical analysis
    1. Nonlinear equations

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cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 41, Issue 3

June 2015

157 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2786970

Editor:
Michael A. Heroux
Sandia National Laboratories, USA

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Copyright © 2015 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 2015

Accepted: 01 September 2014

Revised: 01 January 2014

Received: 01 June 2013

Published in TOMS Volume 41, Issue 3

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Statutory Activities for the Faculty of Electronics
Telecommunication and Informatics
Gdansk University of Technology

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Cited By

Liu XTang DLiu X(2025)An enhanced argument principle algorithm for exact complex transcendental eigenvalue analysis of damped structuresJournal of Sound and Vibration10.1016/j.jsv.2024.118751595(118751)Online publication date: Jan-2025
https://doi.org/10.1016/j.jsv.2024.118751
Trofimowicz DStefański TPietruszka PGulgowski J(2024)Testing Stability of FDTD in Media Described by Time-Fractional Constitutive Relations2024 25th International Microwave and Radar Conference (MIKON)10.23919/MIKON60251.2024.10633996(137-142)Online publication date: 1-Jul-2024
https://doi.org/10.23919/MIKON60251.2024.10633996
Pelloni BSmith D(2024)Revivals, or the Talbot effect, for the Airy equationStudies in Applied Mathematics10.1111/sapm.12699153:2Online publication date: 30-Apr-2024
https://doi.org/10.1111/sapm.12699
Bettemir Ö(2024)Modification of False-Position Method to Improve Its Convergence2024 8th International Artificial Intelligence and Data Processing Symposium (IDAP)10.1109/IDAP64064.2024.10710840(1-6)Online publication date: 21-Sep-2024
https://doi.org/10.1109/IDAP64064.2024.10710840
Wilks BMeylan MMontiel FWakes S(2024)Generalized eigenfunction expansion and singularity expansion methods for two-dimensional acoustic time-domain wave scattering problemsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences10.1098/rspa.2023.0845480:2297Online publication date: 4-Sep-2024
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Theodoulidis TSkarlatos ATytko G(2023)Computation of Eigenvalues and Eigenfunctions in the Solution of Eddy Current ProblemsSensors10.3390/s2306305523:6(3055)Online publication date: 12-Mar-2023
https://doi.org/10.3390/s23063055
Dziedziewicz SWarecka MLech RKowalczyk P(2023)Self-Adaptive Mesh Generator for Global Complex Roots and Poles Finding AlgorithmIEEE Transactions on Microwave Theory and Techniques10.1109/TMTT.2023.323801471:7(2854-2863)Online publication date: Jul-2023
https://doi.org/10.1109/TMTT.2023.3238014
Dziedziewicz SWarecka MLech RKowalczyk P(2023)Global Complex Roots and Poles Finding Algorithm in C × R DomainIEEE Access10.1109/ACCESS.2023.329296111(68809-68817)Online publication date: 2023
https://doi.org/10.1109/ACCESS.2023.3292961
Zhong ZCardoso VMaggio E(2023)Instability of ultracompact horizonless spacetimesPhysical Review D10.1103/PhysRevD.107.044035107:4Online publication date: 16-Feb-2023
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Trofimowicz DStefański T(2021)Testing Stability of Digital Filters Using Optimization Methods with Phase AnalysisEnergies10.3390/en1405148814:5(1488)Online publication date: 9-Mar-2021
https://doi.org/10.3390/en14051488
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