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Iterative refinement of least squares solutions computed from normal equations. (Polish. English summary) Zbl 0701.65028

Let A be an \(m\times n\) matrix, rank \(A=n\), \(n<m\). The author presents an analysis of rounding errors in the solution of the regular linear least squares problem Ax\(\cong b\) using Cholesky decomposition of the normal equation and compares this algorithm with that of Golub-Householder. Then it is shown that the iterative refinement of the solution which uses the standard floating point arithmetics yields almost full accuracy of the computed solution provided a condition of the form \(\nu mn\kappa^ 2<1\) is fulfilled, where \(\kappa =| A| \cdot | A^+|\), \(A^+=(A^ TA)^{-1}A^ T\).
Reviewer: Z.Dostal

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65G50 Roundoff error
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