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Xie, Dongxiu; Xu, An-Bao; Peng, Zhenyun

Least-squares symmetric solution to the matrix equation \(AXB=C\) with the norm inequality constraint. (English) Zbl 1360.65131

Int. J. Comput. Math. 93, No. 9, 1564-1578 (2016).
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)

Cited in 3 Documents

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 algorithm
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References:

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