Polynomial chaos (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Polynomial chaos" in English language version.

refsWebsite

Global rank English rank

14doi.org

2^nd place

5worldcat.org

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4semanticscholar.org

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2harvard.edu

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2sciencedirect.com

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2arxiv.org

69^th place

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1etymonline.com

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1jstor.org

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1web.archive.org

1^st place

1jpier.org

low place

1ssrn.com

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arxiv.org (Global: 69^th place; English: 59^th place)

Alpay, Daniel; Kipnis, Alon (2015). "Wiener Chaos Approach to Optimal Prediction". Numerical Functional Analysis and Optimization. 36 (10): 1286–1306. arXiv:1411.3032. doi:10.1080/01630563.2015.1065273. S2CID 54744829.
Ranftl, Sascha; von der Linden, Wolfgang (2021-11-13). "Bayesian Surrogate Analysis and Uncertainty Propagation". Physical Sciences Forum. 3 (1): 6. arXiv:2101.04038. doi:10.3390/psf2021003006. ISSN 2673-9984.

doi.org (Global: 2^nd place; English: 2^nd place)

doi.org

Wiener, Norbert (1938). "The Homogeneous Chaos". American Journal of Mathematics. 60 (4): 897–936. doi:10.2307/2371268. JSTOR 2371268.
Ghanem, Roger G.; Spanos, Pol D. (1991), "Stochastic Finite Element Method: Response Statistics", Stochastic Finite Elements: A Spectral Approach, New York, NY: Springer New York, pp. 101–119, doi:10.1007/978-1-4612-3094-6_4, ISBN 978-1-4612-7795-8, retrieved 2021-09-29
Xiu, Dongbin; Karniadakis, George Em (2002). "The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations". SIAM Journal on Scientific Computing. 24 (2): 619–644. Bibcode:2002SJSC...24..619X. doi:10.1137/s1064827501387826. ISSN 1064-8275. S2CID 10358251.
Ernst, Oliver G.; Mugler, Antje; Starkloff, Hans-Jörg; Ullmann, Elisabeth (2011-10-12). "On the convergence of generalized polynomial chaos expansions". ESAIM: Mathematical Modelling and Numerical Analysis. 46 (2): 317–339. doi:10.1051/m2an/2011045. ISSN 0764-583X.
Soize, Christian; Ghanem, Roger (2004). "Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure". SIAM Journal on Scientific Computing. 26 (2): 395–410. Bibcode:2004SJSC...26..395S. doi:10.1137/s1064827503424505. ISSN 1064-8275. S2CID 39569403.
"Wiener's Polynomial Chaos for the Analysis and Control of Nonlinear Dynamical Systems with Probabilistic Uncertainties [Historical Perspectives]". IEEE Control Systems. 33 (5): 58–67. 2013. doi:10.1109/MCS.2013.2270410. ISSN 1066-033X. S2CID 5610154.
Enstedt, Mattias; Wellander, Niklas (2016). "Uncertainty Quantification of Radio Propagation Using Polynomial Chaos". Progress in Electromagnetics Research M. 50: 205–213. doi:10.2528/PIERM16062101.
Oladyshkin, S.; Nowak, W. (2012). "Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion". Reliability Engineering & System Safety. 106: 179–190. doi:10.1016/j.ress.2012.05.002.
Oladyshkin, Sergey; Nowak, Wolfgang (2018). "Incomplete statistical information limits the utility of high-order polynomial chaos expansions". Reliability Engineering & System Safety. 169: 137–148. doi:10.1016/j.ress.2017.08.010.
Alpay, Daniel; Kipnis, Alon (2015). "Wiener Chaos Approach to Optimal Prediction". Numerical Functional Analysis and Optimization. 36 (10): 1286–1306. arXiv:1411.3032. doi:10.1080/01630563.2015.1065273. S2CID 54744829.
Ranftl, Sascha; von der Linden, Wolfgang (2021-11-13). "Bayesian Surrogate Analysis and Uncertainty Propagation". Physical Sciences Forum. 3 (1): 6. arXiv:2101.04038. doi:10.3390/psf2021003006. ISSN 2673-9984.

dx.doi.org

Ghanem, Roger G.; Spanos, Pol D. (1991), "Stochastic Finite Element Method: Response Statistics", Stochastic Finite Elements: A Spectral Approach, New York, NY: Springer New York, pp. 101–119, doi:10.1007/978-1-4612-3094-6_4, ISBN 978-1-4612-7795-8, retrieved 2021-09-29
Xiu, Dongbin; Karniadakis, George Em (2002). "The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations". SIAM Journal on Scientific Computing. 24 (2): 619–644. Bibcode:2002SJSC...24..619X. doi:10.1137/s1064827501387826. ISSN 1064-8275. S2CID 10358251.
Soize, Christian; Ghanem, Roger (2004). "Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure". SIAM Journal on Scientific Computing. 26 (2): 395–410. Bibcode:2004SJSC...26..395S. doi:10.1137/s1064827503424505. ISSN 1064-8275. S2CID 39569403.

etymonline.com (Global: 287^th place; English: 321^st place)

The use of the word "chaos" by Norbert Wiener in his 1938 publication precedes the use of "chaos" in the branch of mathematics called chaos theory by almost 40 years. [1]

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Xiu, Dongbin; Karniadakis, George Em (2002). "The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations". SIAM Journal on Scientific Computing. 24 (2): 619–644. Bibcode:2002SJSC...24..619X. doi:10.1137/s1064827501387826. ISSN 1064-8275. S2CID 10358251.
Soize, Christian; Ghanem, Roger (2004). "Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure". SIAM Journal on Scientific Computing. 26 (2): 395–410. Bibcode:2004SJSC...26..395S. doi:10.1137/s1064827503424505. ISSN 1064-8275. S2CID 39569403.

jpier.org (Global: low place; English: low place)

Enstedt, Mattias; Wellander, Niklas (2016). "Uncertainty Quantification of Radio Propagation Using Polynomial Chaos". Progress in Electromagnetics Research M. 50: 205–213. doi:10.2528/PIERM16062101.

jstor.org (Global: 26^th place; English: 20^th place)

Wiener, Norbert (1938). "The Homogeneous Chaos". American Journal of Mathematics. 60 (4): 897–936. doi:10.2307/2371268. JSTOR 2371268.

sciencedirect.com (Global: 149^th place; English: 178^th place)

Oladyshkin, S.; Nowak, W. (2012). "Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion". Reliability Engineering & System Safety. 106: 179–190. doi:10.1016/j.ress.2012.05.002.
Oladyshkin, Sergey; Nowak, Wolfgang (2018). "Incomplete statistical information limits the utility of high-order polynomial chaos expansions". Reliability Engineering & System Safety. 169: 137–148. doi:10.1016/j.ress.2017.08.010.

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Xiu, Dongbin; Karniadakis, George Em (2002). "The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations". SIAM Journal on Scientific Computing. 24 (2): 619–644. Bibcode:2002SJSC...24..619X. doi:10.1137/s1064827501387826. ISSN 1064-8275. S2CID 10358251.
Soize, Christian; Ghanem, Roger (2004). "Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure". SIAM Journal on Scientific Computing. 26 (2): 395–410. Bibcode:2004SJSC...26..395S. doi:10.1137/s1064827503424505. ISSN 1064-8275. S2CID 39569403.
"Wiener's Polynomial Chaos for the Analysis and Control of Nonlinear Dynamical Systems with Probabilistic Uncertainties [Historical Perspectives]". IEEE Control Systems. 33 (5): 58–67. 2013. doi:10.1109/MCS.2013.2270410. ISSN 1066-033X. S2CID 5610154.
Alpay, Daniel; Kipnis, Alon (2015). "Wiener Chaos Approach to Optimal Prediction". Numerical Functional Analysis and Optimization. 36 (10): 1286–1306. arXiv:1411.3032. doi:10.1080/01630563.2015.1065273. S2CID 54744829.

ssrn.com (Global: 703^rd place; English: 501^st place)

papers.ssrn.com

Dias, Fabio; Peters, Gareth W. (2020). Option Pricing with Polynomial Chaos Expansion Stochastic Bridge Interpolators and Signed Path Dependence. p. 11. SSRN 3588871.

web.archive.org (Global: 1^st place; English: 1^st place)

O’Hagan, Anthony. "Polynomial chaos: A tutorial and critique from a statistician’s perspective." SIAM/ASA J. Uncertainty Quantification 20 (2013): 1-20.

worldcat.org (Global: 5^th place; English: 5^th place)

search.worldcat.org

Xiu, Dongbin; Karniadakis, George Em (2002). "The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations". SIAM Journal on Scientific Computing. 24 (2): 619–644. Bibcode:2002SJSC...24..619X. doi:10.1137/s1064827501387826. ISSN 1064-8275. S2CID 10358251.
Ernst, Oliver G.; Mugler, Antje; Starkloff, Hans-Jörg; Ullmann, Elisabeth (2011-10-12). "On the convergence of generalized polynomial chaos expansions". ESAIM: Mathematical Modelling and Numerical Analysis. 46 (2): 317–339. doi:10.1051/m2an/2011045. ISSN 0764-583X.
Soize, Christian; Ghanem, Roger (2004). "Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure". SIAM Journal on Scientific Computing. 26 (2): 395–410. Bibcode:2004SJSC...26..395S. doi:10.1137/s1064827503424505. ISSN 1064-8275. S2CID 39569403.
"Wiener's Polynomial Chaos for the Analysis and Control of Nonlinear Dynamical Systems with Probabilistic Uncertainties [Historical Perspectives]". IEEE Control Systems. 33 (5): 58–67. 2013. doi:10.1109/MCS.2013.2270410. ISSN 1066-033X. S2CID 5610154.
Ranftl, Sascha; von der Linden, Wolfgang (2021-11-13). "Bayesian Surrogate Analysis and Uncertainty Propagation". Physical Sciences Forum. 3 (1): 6. arXiv:2101.04038. doi:10.3390/psf2021003006. ISSN 2673-9984.

Polynomial chaos (English Wikipedia)

arxiv.org (Global: 69th place; English: 59th place)

doi.org (Global: 2nd place; English: 2nd place)

doi.org

dx.doi.org

etymonline.com (Global: 287th place; English: 321st place)

harvard.edu (Global: 18th place; English: 17th place)