Least squares solution of the linear operator equation. (English) Zbl 1350.65032
The paper deals with the least squares solution of the linear operator equation \((*)\) \({\mathcal{F}}(X)=C\), where \({\mathcal{F}}: \mathbb C^{m \times n} \longrightarrow \mathbb C^{p \times q}\) is surjective and \(C \in \mathbb C^{p \times q}\) is given. In this respect, the author extends the classical conjugate gradient least squares algorithm to the new context and proves its convergence to the minimal norm solution of the Problem \((*)\).
Reviewer: Constantin Popa (Constanţa)
MSC:
| 65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
| 15A06 | Linear equations (linear algebraic aspects) |
| 15A24 | Matrix equations and identities |
Keywords:
matrix algorithm; least squares problem; linear operator equation; conjugate gradient least squares algorithm; convergence; minimal norm solutionReferences:
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