Numerical investigations of linear least squares methods for derivative estimation
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Description
The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.
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ID Code: | 30160 | ||||
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Item Type: | Contribution to Journal (Journal Article) | ||||
Refereed: | Yes | ||||
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Keywords: | derivative approximation, least squares, surface fitting, order of magnitude error estimates | ||||
ISSN: | 1446-8735 | ||||
Pure ID: | 60114821 | ||||
Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology Past > Research Centres > CRC for Diagnostics |
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Copyright Owner: | Consult author(s) regarding copyright matters | ||||
Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au | ||||
Deposited On: | 04 Feb 2010 21:53 | ||||
Last Modified: | 04 Mar 2024 14:26 |
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