A certificate for semidefinite relaxations in computing positive-dimensional real radical ideals. (January 2016)

• Record Type: Journal Article
• Authors: Ma, Yue; Wang, Chu; Zhi, Lihong
• Is Part Of: Journal of symbolic computation. Volume 72(2016)
• Page Start: 1
• Page End: 20
• Publication Date: 2016-01
• Subjects: Real radical ideal -- Positive-dimensional ideal -- Semidefinite programming -- Involutive division -- Pommaret basis -- δ-Regular; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2014.12.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: For an ideal I with a positive-dimensional real variety V R ( I ), based on moment relaxations, we study how to compute a Pommaret basis which is simultaneously a Gröbner basis of an ideal J generated by the kernel of a truncated moment matrix and satisfying I ⊆ J ⊆ I ( V R ( I ) ), V R ( I ) = V C ( J ) ∩ R n . We provide a certificate consisting of a condition on coranks of moment matrices for terminating the algorithm. For a generic δ -regular coordinate system, we prove that the condition is satisfiable in a large enough order of moment relaxations.