Sentence examples for completion problem from inspiring English sources

As a corollary, the commutant lifting theorem of Sz.-Nagy and Foia§ is proved by solving a completion problem.

The matrix completion problem min rank ( X ) subject to  X i, j = M i, j, ( i, j ) ∈ Ω, (1.6).

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 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.

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.

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 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.

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.

Therefore, the problems presented in the post-test had different surface features but a similar structure to the problems that were presented in the examples and completion problems.

These scaffolds can be gradually faded as learners acquire more knowledge by presenting them with completion problems after worked examples, for which learners have to fill out missing steps in partially worked-out examples [ 7].