Constructing Dixon Matrix for Sparse Polynomial Equations Based on Hybrid and Heuristics Scheme Article Swipe
Guoqiang Deng
,
Niuniu Qi
,
Min Tang
,
Xuefeng Duan
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.3390/sym14061174
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.3390/sym14061174
Solving polynomial equations inevitably faces many severe challenges, such as easily occupying storage space and demanding prohibitively expensive computation resources. There has been considerable interest in exploiting the sparsity to improve computation efficiency, since asymmetry phenomena are prevalent in scientific and engineering fields, especially as most of the systems in real applications have sparse representations. In this paper, we propose an efficient parallel hybrid algorithm for constructing a Dixon matrix. This approach takes advantage of the asymmetry (i.e., sparsity) in variables of the system and introduces a heuristics strategy. Our method supports parallel computation and has been implemented on a multi-core system. Through time-complexity analysis and extensive benchmarks, we show our new algorithm has significantly reduced computation and memory overhead. In addition, performance evaluation via the Fermat–Torricelli point problem demonstrates its effectiveness in combinatorial geometry optimizations.
Related Topics
Concepts
Heuristics
Computer science
Computation
Overhead (engineering)
Sparse matrix
Matrix (chemical analysis)
Scheme (mathematics)
Algorithm
Polynomial
Mathematical optimization
Theoretical computer science
Mathematics
Operating system
Mathematical analysis
Physics
Materials science
Gaussian
Composite material
Quantum mechanics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/sym14061174
- https://www.mdpi.com/2073-8994/14/6/1174/pdf?version=1654762840
- OA Status
- gold
- Cited By
- 1
- References
- 32
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4282599313
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W4282599313Canonical identifier for this work in OpenAlex
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https://doi.org/10.3390/sym14061174Digital Object Identifier
- Title
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Constructing Dixon Matrix for Sparse Polynomial Equations Based on Hybrid and Heuristics SchemeWork title
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-06-07Full publication date if available
- Authors
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Guoqiang Deng, Niuniu Qi, Min Tang, Xuefeng DuanList of authors in order
- Landing page
-
https://doi.org/10.3390/sym14061174Publisher landing page
- PDF URL
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https://www.mdpi.com/2073-8994/14/6/1174/pdf?version=1654762840Direct link to full text PDF
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://www.mdpi.com/2073-8994/14/6/1174/pdf?version=1654762840Direct OA link when available
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Heuristics, Computer science, Computation, Overhead (engineering), Sparse matrix, Matrix (chemical analysis), Scheme (mathematics), Algorithm, Polynomial, Mathematical optimization, Theoretical computer science, Mathematics, Operating system, Mathematical analysis, Physics, Materials science, Gaussian, Composite material, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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1Total citation count in OpenAlex
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2023: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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