Least squares and the not-Normal Equations
For many of the classic problems of linear algebra, effective and efficient numerical algorithms exist, particularly for situations where dimensions are not too large. <br> The linear least squares problem is one such: excellent algorithms exist when QR factorisation is feasible. However for l...
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2025
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| Summary: | For many of the classic problems of linear algebra, effective and efficient numerical algorithms exist, particularly for situations where dimensions are not too large. <br>
The linear least squares problem is one such: excellent algorithms exist when QR factorisation is feasible. However for large-dimensional (often sparse) linear least squares problems there are currently good solution algorithms only for well-conditioned problems or for problems where there is lots of data but only a few variables in the solution. Such approaches ubiquitously employ Normal Equations and so have to contend with conditioning issues.
<br> We explore some alternative approaches that we characterise as not-Normal Equations where conditioning may not be such an issue |
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