A certificate for semidefinite relaxations in computing positive-dimensional real radical ideals
| Autor: | Lihong Zhi, Chu Wang, Yue Ma |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Semidefinite programming
Discrete mathematics Algebra and Number Theory 010102 general mathematics Moment matrix 010103 numerical & computational mathematics Basis (universal algebra) 01 natural sciences Combinatorics Moment (mathematics) Computational Mathematics Kernel (algebra) Gröbner basis Order (group theory) Ideal (ring theory) 0101 mathematics Mathematics |
| Zdroj: | Journal of Symbolic Computation. 72:1-20 |
| ISSN: | 0747-7171 |
| DOI: | 10.1016/j.jsc.2014.12.002 |
| Popis: | 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 Grobner 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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