Certifying Zeros of Polynomial Systems Using Interval Arithmetic
DC Element | Wert | Sprache |
---|---|---|
dc.contributor.author | Breiding, Paul | |
dc.contributor.author | Rose, Kemal | |
dc.contributor.author | Timme, Sascha | |
dc.date.accessioned | 2023-07-12T06:55:54Z | - |
dc.date.available | 2023-07-12T06:55:54Z | - |
dc.date.issued | 2023 | |
dc.identifier.issn | 0098-3500 | |
dc.identifier.uri | http://osnascholar.ub.uni-osnabrueck.de/handle/unios/71912 | - |
dc.description.abstract | We establish interval arithmetic as a practical tool for certification in numerical algebraic geometry. Our software HomotopyContinuation.jl now has a built-in function certify, which proves the correctness of an isolated nonsingular solution to a square system of polynomial equations. The implementation rests on Krawczyk's method. We demonstrate that it dramatically outperforms earlier approaches to certification. We see this contribution as a powerful new tool in numerical algebraic geometry, which can make certification the default and not just an option. | |
dc.description.sponsorship | Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [445466444, GRK 2434]; European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [787840]; Paul Breiding funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -Projektnummer 445466444; and funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 787840). Sascha Timme supported by the Deutsche Forschungsgemeinschaft (German Research Foundation) Graduiertenkolleg Facets of Complexity (GRK 2434). | |
dc.language.iso | en | |
dc.publisher | ASSOC COMPUTING MACHINERY | |
dc.relation.ispartof | ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE | |
dc.subject | Computer Science | |
dc.subject | Computer Science, Software Engineering | |
dc.subject | Datasets | |
dc.subject | gaze detection | |
dc.subject | HOMOTOPY CONTINUATION | |
dc.subject | Mathematics | |
dc.subject | Mathematics, Applied | |
dc.subject | neural networks | |
dc.subject | text tagging | |
dc.title | Certifying Zeros of Polynomial Systems Using Interval Arithmetic | |
dc.type | journal article | |
dc.identifier.doi | 10.1145/3580277 | |
dc.identifier.isi | ISI:000952028100011 | |
dc.description.volume | 49 | |
dc.description.issue | 1 | |
dc.contributor.researcherid | AAD-4179-2020 | |
dc.identifier.eissn | 1557-7295 | |
dc.publisher.place | 1601 Broadway, 10th Floor, NEW YORK, NY USA | |
dcterms.isPartOf.abbreviation | ACM Trans. Math. Softw. | |
dcterms.oaStatus | Green Submitted | |
local.import.remains | affiliations : University Osnabruck; Technical University of Berlin | |
local.import.remains | web-of-science-index : Science Citation Index Expanded (SCI-EXPANDED) | |
crisitem.author.dept | FB 06 - Mathematik/Informatik/Physik | - |
crisitem.author.deptid | fb6 | - |
crisitem.author.orcid | 0000-0003-3747-9185 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | BrPa211 | - |
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geprüft am 01.06.2024