This issue is shown to boil down to a matrix completion problem subject to given constraint of hermitian symmetry, measurements fitting, reduced rank and spatial continuity of the sound field.
We study the completion problem to an invertible operator-valued function for the class of bounded holomorphic functions on the unit disk D⊂S with relatively compact images in the space of bounded linear operators between complex Banach spaces.
In particular, we prove that in this class of functions the operator-valued corona problem and the completion problem are not equivalent, and establish an Oka-type principle asserting that the completion problem is solvable if and only if it is solvable in the class of continuous operator-valued functions on D with relatively compact images.
The numerical results on the matrix completion problem with noisy measurements indicate that our algorithm gives a more accurate reconstruction and takes less time compared with some other existing algorithms.
The maximum entropy completion problem for block-circulant matrices has recently been solved by the authors, although leaving open the problem of an efficient computation of the solution.
The matrix completion problem min rank ( X ) subject to X i, j = M i, j, ( i, j ) ∈ Ω, (1.6).
For simple "matrix completion problem", Cai et al. proves that when the step length δ is between 0.5 and 2, the algorithm converges definitely [ 26].
On a Thursday late last month just before Natalie took the test, her tutor handed her a packet of pattern completion problems and started to explain the directions.
We characterize the solvability of such (0,1 -matrix completion problems via the nonnegativity of a structure tensor which is defined in terms of the problem parameters: the row sums, column sums, and the positions of fixed zeros.
We have found that this procedure actually discovers the classic theorem in a modest collection of classic cases involving factorization of engineering systems and matrix completion problems.
