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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| _version_ | 1824459193692717056 |
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| author | Wathen, AJ |
| author_facet | Wathen, AJ |
| author_sort | Wathen, AJ |
| collection | OXFORD |
| description | 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 |
| first_indexed | 2025-02-19T04:37:54Z |
| format | Journal article |
| id | oxford-uuid:69c498d1-3341-47b6-8a15-66ca82dc1c21 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-02-19T04:37:54Z |
| publishDate | 2025 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:69c498d1-3341-47b6-8a15-66ca82dc1c212025-02-10T15:28:28ZLeast squares and the not-Normal EquationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:69c498d1-3341-47b6-8a15-66ca82dc1c21EnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2025Wathen, AJFor 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 |
| spellingShingle | Wathen, AJ Least squares and the not-Normal Equations |
| title | Least squares and the not-Normal Equations |
| title_full | Least squares and the not-Normal Equations |
| title_fullStr | Least squares and the not-Normal Equations |
| title_full_unstemmed | Least squares and the not-Normal Equations |
| title_short | Least squares and the not-Normal Equations |
| title_sort | least squares and the not normal equations |
| work_keys_str_mv | AT wathenaj leastsquaresandthenotnormalequations |