Content deleted Content added
m significative replace |
→Further reading: rm deadlink that just goes to the same place as the doi |
||
| (2 intermediate revisions by 2 users not shown) | |||
Line 31:
&= \left [\mathbf y - \mathbf f\left (\boldsymbol\beta\right )\right ]^{\mathrm T}\left [\mathbf y - \mathbf f\left (\boldsymbol\beta\right )\right ] - 2\left [\mathbf y - \mathbf f\left (\boldsymbol\beta\right )\right ]^{\mathrm T} \mathbf J \boldsymbol\delta + \boldsymbol\delta^{\mathrm T} \mathbf J^{\mathrm T} \mathbf J\boldsymbol\delta.
\end{align}</math>
Taking the derivative of this approximation of <math>S\left (\boldsymbol\beta + \boldsymbol\delta\right )</math> with respect to {{tmath|\boldsymbol\delta}} and setting the result to zero gives
:<math>\left (\mathbf J^{\mathrm T} \mathbf J\right )\boldsymbol\delta = \mathbf J^{\mathrm T}\left [\mathbf y - \mathbf f\left (\boldsymbol\beta\right )\right ],</math>
Line 204:
|number = 4
|pages = W1–W16
|bibcode = 2007Geop...72W...1P
}}
* {{cite book
| last1 = Nocedal | first1 = Jorge
Line 219 ⟶ 218:
== External links ==
* Detailed description of the algorithm can be found in [
* C. T. Kelley, ''Iterative Methods for Optimization'', SIAM Frontiers in Applied Mathematics, no 18, 1999, {{isbn|0-89871-433-8}}. [http://www.siam.org/books/textbooks/fr18_book.pdf Online copy]
* [https://web.archive.org/web/20140301154319/http://www3.villanova.edu/maple/misc/mtc1093.html History of the algorithm in SIAM news]
| |||