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A geometric property of the least squares solution of linear equations. (English) Zbl 0704.15005
The authors consider the overdetermined system of linear equations \(Ax=b\), where A is an \(m\times n\) real matrix for some \(m>n\), and presents a new representation of the solution of the least squares problem: \[ \min \{(Ax-b)^ T(Ax-b)=\| Ax-b\|^ 2_ 2;\quad x\in R^ n\}. \]
Reviewer: K.Burian

MSC:
15A09 Theory of matrix inversion and generalized inverses
65F20 Numerical solutions to overdetermined systems, pseudoinverses
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