Name
Abstract | ||
|---|---|---|
This note studies the problem of nonsymmetric rank-one matrix completion. We show that in every instance where the problem has a unique solution, one can recover the original matrix through the second round of the sum-of-squares/Lasserre hierarchy with minimization of the trace of the moments matrix. Our proof system is based on iteratively building a sum of N - 1 linearly independent squares, where N is the number of monomials of degree at most two, corresponding to the canonical basis (z
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup>
- z
<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub>
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup>
)
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>
. Those squares are constructed from the ideal I generated by the constraints and the monomials provided by the minimization of the trace. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1109/CAMSAP.2015.7383723 | 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) |
Keywords | Field | DocType |
sum-of-squares relaxation,nonsymmetric rank-one matrix completion,Lasserre hierarchy,moment matrix minimization,proof system,N-1 linearly independent squares | Discrete mathematics,Standard basis,Linear independence,Combinatorics,Matrix completion,Matrix (mathematics),Single-entry matrix,Symmetric matrix,Convex function,Explained sum of squares,Mathematics | Conference |
Citations | PageRank | References |
1 | 0.36 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Augustin Cosse | 1 | 1 | 0.36 |
| Laurent Demanet | 2 | 750 | 57.81 |