Least-squares symmetric solution to the matrix equation \(AXB=C\) with the norm inequality constraint. (English) Zbl 1360.65131
The authors consider the least squares problem with the norm inequality constraints
\[
\min_{X \in S\mathbb{R}^{n \times n}} \frac{1}{2}\| AXB- C\|\text{ subject ~to }\| X\| \leq \Delta,
\]
with \(A, B, C\) corresponding matrices and \(\Delta\) a non-negative real number. They propose a new matrix-form iterative method based on the Lanczos trust region algorithm.
Reviewer: Constantin Popa (Constanţa)
MSC:
65F30 | Other matrix algorithms (MSC2010) |
65F10 | Iterative numerical methods for linear systems |
15A24 | Matrix equations and identities |
65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
Keywords:
matrix equation; iterative method; norm-constrained problem; symmetric least squares problem; norm inequality constraints; Lanczos trust region algorithmReferences:
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