J.B. Lasserre. Polynomials nonnegative on a grid and discrete representations. Transactions of the American Mathematical Society, 354:631--649, 2001. Home/Search Document Not in Database Summary Related Articles Check |
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Semidefinite Representations for Finite Varieties - Laurent (2003) (Correct)
.... condition) then every positive polynomial on F has a decomposition (6) This result implies the asymptotic convergence of the lower bounds # # t , p # t to p # as t goes to infinity [11] In the special case when F is contained in or is equal to the set of points in a grid, Lasserre [12, 13] shows the finite convergence of the bounds # # t , p # t to p # . His proof is based on a result by Curto and Fialkow [5, 6] about flat extensions of moment matrices (which uses the Riesz representation theorem) see Corollary 13) As a consequence, every polynomial nonnegative on F has a ....
.... finite convergence of the Lasserre relaxations (5) The formulation does not contain any semidefinite constraint for the equations h j (x) 0 (j m) as they have already been used for the construction of the moment matrix M (y) Such concise representation was mentioned in the grid case ([8, 9, 13]) Equivalence of (1) and (21) is an easy result, which follows from a simple combinatorial identity involving the Zeta matrix of the ideal (see Lemma 6) this is a direct extension of the corresponding result given in [15] and [8] for the 0 1 and cases (which also underlies the convergence ....
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J.B. Lasserre. Polynomials nonnegative on a grid and discrete representations. Transactions of the American Mathematical Society, 354:631--649, 2001.
Semidefinite Representations for Finite Varieties - Laurent (2004) (Correct)
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J.B. Lasserre. Polynomials nonnegative on a grid and discrete representations. Transactions of the American Mathematical Society, 354:631--649, 2001.
Revisiting Two Theorems of Curto and Fialkow on Moment Matrices - Laurent (2004) (Correct)
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J.B. Lasserre. Polynomials nonnegative on a grid and discrete representations. Trans. Amer. Math. Soc. 354 (2001), 631--649.
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