Inverse singular value problems have been a research focus for decades. It is true that an inverse singular value problem is trivial if the desired matrix is not restricted to any structure. This paper presents a numerical procedure, based on an alternating projection process, for solving inverse singular value problems for nonnegative matrices subject to given diagonal entries. In theory, the necessary and sufficient conditions for the existence of nonnegative 2 × 2 matrices subject to prescribed singular values and diagonal entries are derived. Although the focus of this paper is on inverse singular value problems with prescribed diagonal entries, the entire procedure can be straightforwardly applied to other types of structure. Numerical examples are used to demonstrate the capacity and efficiency of our method.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Signal Processing
- Mathematical Physics
- Computer Science Applications
- Applied Mathematics