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Limits of Positive Flat Moment Matrices

Lawrence Fialkow
Department of Computer Science, SUNY


Corresponding to an n-dimensional real multisequence y of degree 2d is the moment matrix M_d(y). The property that M_d(y) is positive semidefinite and and flat, i.e., rank M_d = rank M_{d-1}, provides a concrete condition for the existence of a representing measure for y. We discuss membership in the closure of the positive flat moment matrices, which provides approximate representing measures. In previous work with J. Nie, we showed that for n=1 or n=d=2, M_d is in the closure if and only if M_d\succeq 0 and rank M_d\le size(M_{d-1}. We extend this result to n=2, d=3 within the framework of a general condition for membership in the closure.

Tuesday, January 15, 2013
11:00AM AP&M 2402