On singular values of partially prescribed matrices (Q947678)

Motivated by problems coming from computer vision, this paper solves the problem of determining the possible values of the \(p\)th singular value of a partially prescribed matrix in the case when the set of unknown entries has the form of a Young diagram. A complete solution for the generic matrix is given. It is shown that an arbitrary matrix can be completed such that the resulting matrix has the \(p\)th singular value arbitrarily close to a theoretical minimum. A fast and efficient algorithm for the determination of the unknown entries is provided. A second problem of determining the possible \(p\)th singular value of a given matrix under a specified rank one perturbation is solved.