Open weak CAD and its applications.
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| Title: | Open weak CAD and its applications. |
|---|---|
| Authors: | Han, Jingjun1 hanjingjunfdfz@gmail.com, Dai, Liyun1 dailiyun@pku.edu.cn, Hong, Hoon2 hong@ncsu.edu, Xia, Bican3 xbc@math.pku.edu.cn |
| Source: | Journal of Symbolic Computation. May2017 Part 3, Vol. 80, p785-816. 32p. |
| Subjects: | Computer-aided design, Polynomials, Symbolic computation, Applied mathematics, Mathematical analysis |
| Abstract: | The concept of open weak CAD is introduced. Every open CAD is an open weak CAD. On the contrary, an open weak CAD is not necessarily an open CAD. An algorithm for computing projection polynomials of open weak CADs is proposed. The key idea is to compute the intersection of projection factor sets produced by different projection orders. The resulting open weak CAD often has smaller number of sample points than open CADs. The algorithm can be used for computing sample points for all open connected components of f ≠ 0 for a given polynomial f . It can also be used for many other applications, such as testing semi-definiteness of polynomials and copositive problems. In fact, we solved several difficult semi-definiteness problems efficiently by using the algorithm. Furthermore, applying the algorithm to copositive problems, we find an explicit expression of the polynomials producing open weak CADs under some conditions, which significantly improves the efficiency of solving copositive problems. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Symbolic Computation is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 119653738 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Open weak CAD and its applications. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Han%2C+Jingjun%22">Han, Jingjun</searchLink><relatesTo>1</relatesTo><i> hanjingjunfdfz@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Dai%2C+Liyun%22">Dai, Liyun</searchLink><relatesTo>1</relatesTo><i> dailiyun@pku.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Hong%2C+Hoon%22">Hong, Hoon</searchLink><relatesTo>2</relatesTo><i> hong@ncsu.edu</i><br /><searchLink fieldCode="AR" term="%22Xia%2C+Bican%22">Xia, Bican</searchLink><relatesTo>3</relatesTo><i> xbc@math.pku.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Symbolic+Computation%22">Journal of Symbolic Computation</searchLink>. May2017 Part 3, Vol. 80, p785-816. 32p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Computer-aided+design%22">Computer-aided design</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Symbolic+computation%22">Symbolic computation</searchLink><br /><searchLink fieldCode="DE" term="%22Applied+mathematics%22">Applied mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The concept of open weak CAD is introduced. Every open CAD is an open weak CAD. On the contrary, an open weak CAD is not necessarily an open CAD. An algorithm for computing projection polynomials of open weak CADs is proposed. The key idea is to compute the intersection of projection factor sets produced by different projection orders. The resulting open weak CAD often has smaller number of sample points than open CADs. The algorithm can be used for computing sample points for all open connected components of f ≠ 0 for a given polynomial f . It can also be used for many other applications, such as testing semi-definiteness of polynomials and copositive problems. In fact, we solved several difficult semi-definiteness problems efficiently by using the algorithm. Furthermore, applying the algorithm to copositive problems, we find an explicit expression of the polynomials producing open weak CADs under some conditions, which significantly improves the efficiency of solving copositive problems. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Symbolic Computation is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jsc.2016.07.032 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 32 StartPage: 785 Subjects: – SubjectFull: Computer-aided design Type: general – SubjectFull: Polynomials Type: general – SubjectFull: Symbolic computation Type: general – SubjectFull: Applied mathematics Type: general – SubjectFull: Mathematical analysis Type: general Titles: – TitleFull: Open weak CAD and its applications. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Han, Jingjun – PersonEntity: Name: NameFull: Dai, Liyun – PersonEntity: Name: NameFull: Hong, Hoon – PersonEntity: Name: NameFull: Xia, Bican IsPartOfRelationships: – BibEntity: Dates: – D: 03 M: 05 Text: May2017 Part 3 Type: published Y: 2017 Identifiers: – Type: issn-print Value: 07477171 Numbering: – Type: volume Value: 80 Titles: – TitleFull: Journal of Symbolic Computation Type: main |
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