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- Title
Lebesgue decomposition in action via semidefinite relaxations.
- Authors
Lasserre, Jean
- Abstract
Given all (finite) moments of two measures μ and λ on $\mathbb {R}^{n}$ , we provide a numerical scheme to obtain the Lebesgue decomposition μ = ν + ψ with ν≪ λ and ψ ⊥ λ. When ν has a density in $L_{\infty }(\lambda )$ then we obtain two sequences of finite moments vectors of increasing size (the number of moments) which converge to the moments of ν and ψ respectively, as the number of moments increases. Importantly, no à priori knowledge on the supports of μ, ν and ψ is required.
- Subjects
MATHEMATICAL decomposition; MOMENT problems (Mathematics); VECTORS (Calculus)
- Publication
Advances in Computational Mathematics, 2016, Vol 42, Issue 5, p1129
- ISSN
1019-7168
- Publication type
Article
- DOI
10.1007/s10444-016-9456-1