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We establish a connection between multiplication operators and shift operators. Moreover, we derive positive semidefinite conditions of finite rank moment sequences and use these conditions to strengthen Lasserre's hierarchy for real and complex polynomial optimization. Integration of the strengthening technique with sparsity is considered. Extensi...
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... solve each instance using the dense LAS (with the above monomial basis) at r = 2, the sparse LAS (with the above monomial basis) at r = 2, s = 1, and the sparse S-LAS (with the above monomial basis) at r = 2, respectively. The results are presented in Table 2 from which we can see that the strengthening technique improves the bound provided by the sparse LAS while it is much cheaper than the dense LAS. 6.3. ...Similar publications
We present an adapted construction of algebraic circuits over the reals introduced by Cucker and Meer to arbitrary infinite integral domains and generalize the $\mathrm{AC}_{\mathbb{R}}$ and $\mathrm{NC}_{\mathbb{R}}^{}$ classes for this setting. We give a theorem in the style of Immerman’s theorem which shows that for these adapted formalisms, set...
