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Polynomial and rational function modeling: Difference between revisions

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==See also==
* [[Response surface methodology]]
* [[Padé approximant|Pade Approximant]]
 
==Bibliography==
* {{cite book |author=[http://stats.lse.ac.uk/atkinson/ Atkinson, A. C.] and [http://www.maths.manchester.ac.uk/~adonev/ |author2=Donev, A. N.] and [http://support.sas.com/publishing/bbu/companion_site/index_author.html#tobias |author3=Tobias, R. D.]|title=Optimum Experimental Designs, with SAS| url=https://books.google.com/books?id=oIHsrw6NBmoC| publisher=Oxford University Press|year=2007 |pages=511+xvi |isbn=978-0-19-929660-6 |oclc= |doi=}}
* Box, G. E. P. and Draper, Norman. 2007. ''Response Surfaces, Mixtures, and Ridge Analyses'', Second Edition [of ''Empirical Model-Building and Response Surfaces'', 1987], Wiley.
* {{cite book |authorlinkauthor-link=Jack Kiefer (statistician)| last=Kiefer| first=Jack Carl| title=Collected Papers III Design of Experiments |editorlinkeditor-link=Lawrence D. Brown| editor=L. D. Brown|publisher=Springer-Verlag|year=1985|isbn=978-0-387-96004-X3|display-editors=etal}}
* R. H. Hardin and [[Neil Sloane|N. J. A. Sloane]], [http://neilsloane.com/doc/design.pdf "A New Approach to the Construction of Optimal Designs", ''Journal of Statistical Planning and Inference'', vol. 37, 1993, pp. 339-369]
* R. H. Hardin and [[Neil Sloane|N. J. A. Sloane]], [http://neilsloane.com/doc/doeh.pdf "Computer-Generated Minimal (and Larger) Response Surface Designs: (I) The Sphere"]
* R. H. Hardin and [[Neil Sloane|N. J. A. Sloane]], [http://neilsloane.com/doc/meatball.pdf "Computer-Generated Minimal (and Larger) Response Surface Designs: (II) The Cube"]
* {{Cite book| title=Design and Analysis of Experiments | series=Handbook of Statistics| volume=13|editor=Ghosh, S. |editor2=[[Calyampudi Radhakrishna Rao|Rao, C. R.]] |editor2-link=Calyampudi Radhakrishna Rao | publisher=North-Holland| year=1996| isbn=978-0-444-82061-27}}
** {{Cite book|author1=Draper, Norman |author2=Lin, Dennis K. J. |lastauthorampname-list-style=yesamp | chapter=Response Surface Designs |pages=343–375}}
** {{Cite book|author1=Gaffke, N. |author2=Heiligers, B |lastauthorampname-list-style=yesamp | chapter=Approximate Designs for [[Linear regression|Polynomial Regression]]: [[Invariant estimator|Invariance]], [[Admissible decision rule|Admissibility]], and [[Optimal design|Optimality]] |pages=1149–1199}}
* {{cite book |author=Melas, Viatcheslav B.|title=Functional Approach to Optimal Experimental Design |series=Lecture Notes in Statistics| volume=184 | publisher=Springer-Verlag | year=2006 |isbn=978-0-387-98741-X5}} (Modeling with rational functions)
 
===Historical===
*{{cite journal
|title=Application de la méthode des moindre quarrés a l'interpolation des suites<!-- [The application of the method of least squares to the interpolation of sequences] -->
|author=[[Joseph Diaz Gergonne|Gergonne, J. D.]]
|journal=[[Annales de mathématiques pures et appliquées]]
|volume=6
|year=1815
|pages=242–252
|author-link=Joseph Diaz Gergonne
}}
*{{cite journal
|title=The application of the method of least squares to the interpolation of sequences
|author=[[Joseph Diaz Gergonne|Gergonne, J. D.]]
|journal=Historia Mathematica
|volume=1
|issue=4 <!-- |month=November -->
|year=1974 |origyearorig-year=1815
|pages=439–447
|edition=Translated by Ralph St. John and [[Stephen M. Stigler|S. M. Stigler]] from the 1815 French
|doi=10.1016/0315-0860(74)90034-2
|author-link=Joseph Diaz Gergonne
|url=http://www.sciencedirect.com/science/article/B6WG9-4D7JMHH-20/2/df451ec5fbb7c044d0f4d900af80ec86
|doi-access=free
}}
*{{cite journal
|title=Gergonne's 1815 paper on the design and analysis of polynomial regression experiments
|author=[[Stephen M. Stigler|Stigler, Stephen M.]]
|journal=[[Historia Mathematica]]
|volume=1
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|pages=431–439
|doi=10.1016/0315-0860(74)90033-0
|author-link=Stephen M. Stigler
|url=http://www.sciencedirect.com/science/article/B6WG9-4D7JMHH-1Y/2/680c7ada0198761e9866197d53512ab4}}
|doi-access=free
}}
* {{cite journal
|author=Smith, Kirstine
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|issue=1/2
|pages=1–85
|url=http://biomet.oxfordjournals.org/cgi/content/citation/12/1-2/1
|jstor=2331929
|doi=10.1093/biomet/12.1-2.1}}
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