A direct method for sparse least squares problems with lower and upper bounds (Q1112557)
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scientific article; zbMATH DE number 4078638
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A direct method for sparse least squares problems with lower and upper bounds |
scientific article; zbMATH DE number 4078638 |
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A direct method for sparse least squares problems with lower and upper bounds (English)
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1988
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The least squares problem \(\| Ax-b\|_ 2\to Min\). (the solution of which being subject to the additional restriction \(1\leq x\leq u)\) is solved by QR-factorization (using SPARSEPAK), followed by a stable updating procedure for R. The main point is that the updating avoids fill-in and uses the fixed data structure of the factor R. Comparing numerical tests between the new method and the algorithm NNLS of \textit{C. L. Lawson} and \textit{R. J. Hanson} (Solving least squares problems. (1974; M.R. 51.2270)] show remarkable savings both in CPU-time and in storage requirements.
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sparse matrices
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fill-in comparison of methods
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least squares problem
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QR-factorization
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stable updating
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numerical tests
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M.R. 51.2270
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