The truncated complex -moment problem

By R. Curto, L. Fialkow. 2000

122 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/fca392fa288e491b82a153ebb83b6d8b8659e26a

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In Algebra and Number Theory

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Bounds on measures satisfying moment conditions (2002, background): “1 in [5], is stated in dimension 2 for the complex plane, but is valid for n real or complex variables; see comments on page 2 in [5].”
Truncated K-moment problems in several variables (2005, methodology): “hat, placing more emphasis on the abstract properties of ﬂat extensions and less emphasis on detailed calculations of the extensions; such calculations unnecessarily complicated the argument given in [CuFi4]. Theorem 4.1 is the main technical result that we need to prove Theorem 1.1. In the followin”
An analogue of the Riesz–Haviland theorem for the truncated moment problem (2008, methodology): “Proof. Assume that M(n) 0 is positive and recursively generated, Mq(n) 0 and M q(n) 0. It follows that Mq(n) = 0, so we conclude thatq(X,Y ) aX+bY +c1 = 0, using the real version of [ CF5 , Proposition 3.9(i)-(ii)].”
Detecting global optimality and extracting solutions in GloptiPoly (2003, background): “6 in [6], y∗ is the vector of moments of a rankMk(y ∗)-atomic measure supported on the feasible set K = {x ∈ R | gi(x) ≥ 0, i = 1, .”
An Explicit Exact SDP Relaxation for Nonlinear 0-1 Programs (2001, background): “Moreover, from the constraints Mn+v vk (gky) 0, for all k =1 ;:::m +2n, it also follows that y is supported on IK. Theorem 1.6 in Curto and Fialkow [ 1 ] is stated in dimension 2 for the complex plane, but is valid for n real or complex variables (see comments page 2 in [1]).”
A generalized flat extension theorem for moment matrices (2009, unknown): “[4–6] and further references therein).”
Revisiting two theorems of Curto and Fialkow on moment matrices (2005, methodology): “The following is the main result of [10] (Theorem 1.”
Polynomials nonnegative on a grid and discrete optimization (2001, methodology): “In the terminology of Curto and Fialkow [2], Mr+v−vk(gky) is well-defined relative to the unique flat extension Mr+v(y) of Mr(y).”