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[ACM Press the 36th international symposium - San Jose, California, USA (2011.06.08-2011.06.11)] Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11 - The minimum-rank gram matrix completion via modified fixed point continuation method

✍ Scribed by Ma, Yue; Zhi, Lihong

Book ID
121870109
Publisher
ACM Press
Year
2011
Weight
479 KB
Category
Article
ISBN
1450306756

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[ACM Press the 36th international sympos
[ACM Press the 36th international symposium - San Jose, California, USA (2011.06.08-2011.06.11)] Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11 - The minimum-rank gram matrix completion via modified fixed point continuation method
✍ Ma, Yue; Zhi, Lihong πŸ“‚ Article πŸ“… 2011 πŸ› ACM Press 🌐 English βš– 479 KB

The problem of computing a representation for a real polynomial as a sum of minimum number of squares of polynomials can be casted as finding a symmetric positive semidefinite real matrix of minimum rank subject to linear equality constraints. In this paper, we propose algorithms for solving the min

[ACM Press the 36th international sympos
[ACM Press the 36th international symposium - San Jose, California, USA (2011.06.08-2011.06.11)] Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11 - Fast algorithm for change of ordering of zero-dimensional GrΓΆbner bases with sparse multiplication matrices
✍ FaugΓ¨re, Jean-Charles; Mou, Chenqi πŸ“‚ Article πŸ“… 2011 πŸ› ACM Press 🌐 English βš– 433 KB

Let I βŠ‚ K[x 1 ,...,x n ] be a 0-dimensional ideal of degree D where K is a field. It is well-known that obtaining efficient algorithms for change of ordering of GrΓΆbner bases of I is crucial in polynomial system solving. Through the algorithm FGLM, this task is classically tackled by linear algebra