Search Results - "multivariate polynomial approximation"

Uniqueness of solutions in multivariate Chebyshev approximation problems

Authors: Vera Roshchina Nadezda Sukhorukova Julien Ugon

Subject Terms: Mathematical sciences, Applied mathematics, Numerical and computational mathematics, Pure mathematics, ALGORITHM, Chebyshev approximation, Mathematics, Applied, Multivariate polynomial approximation, Operations Research & Management Science, Physical Sciences, Science & Technology, Technology, Uniqueness of solutions

Relation: http://hdl.handle.net/10779/DRO/DU:24165987.v1; https://figshare.com/articles/journal_contribution/Uniqueness_of_solutions_in_multivariate_Chebyshev_approximation_problems/24165987

Availability: http://hdl.handle.net/10779/DRO/DU:24165987.v1
https://figshare.com/articles/journal_contribution/Uniqueness_of_solutions_in_multivariate_Chebyshev_approximation_problems/24165987

Optimal polynomial admissible meshes on some classes of compact subsets of Rd

Authors: Piazzon, Federico

Source: Journal of Approximation Theory. 207:241-264

Subject Terms: FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Admissible meshes, Distance function, Multivariate polynomial approximation, Positive reach, Analysis, Numerical Analysis, Mathematics (all), Applied Mathematics, 0101 mathematics, 16. Peace & justice, 01 natural sciences

Access URL: http://arxiv.org/abs/1302.4718
http://ui.adsabs.harvard.edu/abs/2013arXiv1302.4718P/abstract
https://dblp.uni-trier.de/db/journals/jat/jat207.html#Piazzon16
https://core.ac.uk/display/154331006
https://www.sciencedirect.com/science/article/abs/pii/S0021904516000381
https://www.sciencedirect.com/science/article/pii/S0021904516000381
https://hdl.handle.net/11577/3265895
http://www.elsevier.com/inca/publications/store/6/2/2/8/5/3/index.htt
https://doi.org/10.1016/j.jat.2016.02.015

Bivariate generalized Bernstein operators and their application to Fredholm integral equations

Authors: OCCORSIO, Donatella RUSSO, Maria Grazia Occorsio, Donatella et al.

Contributors: OCCORSIO, Donatella RUSSO, Maria Grazia Occorsio, Donatella et al.

Source: Publications de l'Institut Mathematique. 100:141-162

Subject Terms: Multivariate polynomial approximation, Cubature formula, 4. Education, Mathematics (all), 0101 mathematics, Iterated Bernstein polynomial, Nyström method, 01 natural sciences

Access URL: http://www.doiserbia.nb.rs/ft.aspx?id=0350-13021614141O
http://www.doiserbia.nb.rs/Article.aspx?ID=0350-13021614141O
https://iris.unibas.it/handle/11563/125006

Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients

Authors: J. Beck NOBILE, FABIO TAMELLINI, LORENZO et al.

Source: ESAIM: Proceedings. 33:10-21

Subject Terms: 0101 mathematics, Uncertainty Quantification, PDEs with random data, elliptic equations, multivariate polynomial approximation, \bMt approximation, Stochastic Galerkin methods, Smolyak approximation, Sparse grids, Stochastic Collocation methods, 01 natural sciences

Access URL: https://www.esaim-proc.org/articles/proc/pdf/2011/04/proc113302.pdf
http://www.esaim-proc.org/index.php?option=com_article&access=doi&doi=10.1051/proc/201133002&Itemid=129
https://hdl.handle.net/11311/622765

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Authors: Migliorati, Giovanni Nobile, Fabio Tempone, Raul et al.

Contributors: Migliorati, Giovanni Nobile, Fabio Tempone, Raul et al.

Source: Journal of Multivariate Analysis

Subject Terms: Multivariate polynomial approximation, Large deviations, Learning theory, Error analysis, Approximation theory, Discrete least squares, Convergence rates, Noisy evaluations, 0101 mathematics, 16. Peace & justice, 01 natural sciences

File Description: application/pdf

Access URL: https://www.sciencedirect.com/science/article/pii/S0047259X15001931
https://ideas.repec.org/a/eee/jmvana/v142y2015icp167-182.html
https://infoscience.epfl.ch/record/205816
http://www.sciencedirect.com/science/article/pii/S0047259X15001931
https://repository.kaust.edu.sa/bitstream/10754/576075/1/1-s2.0-S0047259X15001931-main.pdf
https://dblp.uni-trier.de/db/journals/ma/ma142.html#MiglioratiNT15

Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients

Authors: Fabio Nobile Raul Tempone Applied Mathematics and Computational Science Program et al.

Contributors: Fabio Nobile Raul Tempone Applied Mathematics and Computational Science Program et al.

Source: International Journal for Numerical Methods in Engineering. 80:979-1006

Subject Terms: Multivariate polynomial approximation, Stochastic Collocation methods, Parabolic equations, PDEs with random data • parabolic equations • multivariate polynomial approximation • Stochastic Galerkin methods • Stochastic Collocation methods • sparse grids • Smolyak approximation • Point Collocation • Monte Carlo sampling, PDEs with random data, Point Collocation, Sparse grids, 0101 mathematics, Stochastic galerkin methods, 01 natural sciences, Smolyak approximation, Monte carlo sampling

Access URL: https://infoscience.epfl.ch/record/180349
https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.2656
http://onlinelibrary.wiley.com/doi/10.1002/nme.2656/abstract
http://www.diva-portal.org/smash/record.jsf?pid=diva2:411086
https://re.public.polimi.it/handle/11311/533391
http://ui.adsabs.harvard.edu/abs/2009IJNME..80..979N/abstract

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Authors: Lorenzo Tamellini Fabio Nobile Joakim Beck et al.

Contributors: Lorenzo Tamellini Fabio Nobile Joakim Beck et al.

Source: Computers & Mathematics with Applications. 67:732-751

Subject Terms: Multivariate polynomial approximation, Subexponential convergence, Elliptic PDEs with random data, Stochastic Galerkin method, 8. Economic growth, Best M-terms polynomial approximation, 0101 mathematics, 16. Peace & justice, 01 natural sciences, Uncertainty quantification

Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0898122113001569
https://www.sciencedirect.com/science/article/pii/S0898122113001569
http://mathicse.epfl.ch/files/content/sites/mathicse/files/Mathicse%20reports%202012/24.2012_JB-FN-LT-RT.pdf
https://dblp.uni-trier.de/db/journals/cma/cma67.html#BeckNTT14
https://infoscience.epfl.ch/record/180948

Asymptotic expansions for multivariate polynomial approximation

Authors: Walz, Guido

Source: Journal of Computational and Applied Mathematics. 122:317-328

Subject Terms: Bernstein operator, asymptotic expansion, Applied Mathematics, Extrapolation, Multidimensional problems, extrapolation, Asymptotic expansion, 01 natural sciences, Multivariate polynomial approximation, Computational Mathematics, Approximation by polynomials, Convergence acceleration, convergence acceleration, 0101 mathematics, multivariate polynomial approximation

File Description: application/xml

Access URL: https://ui.adsabs.harvard.edu/abs/2000JCoAM.122..317W/abstract
https://www.sciencedirect.com/science/article/pii/S0377042700003587
https://dialnet.unirioja.es/servlet/articulo?codigo=700168
https://madoc.bib.uni-mannheim.de/1597/

Increasing the polynomial reproduction of a quasi-interpolation operator

Authors: Shayne Waldron

Source: Journal of Approximation Theory. 161:114-126

Subject Terms: Finite element method, Mathematics(all), Numerical Analysis, Chu–Vandermonde convolution, Applied Mathematics, Lagrange interpolation, Quasi-interpolation, 01 natural sciences, Multivariate polynomial approximation, Bernstein polynomial, Multipoint Taylor formula, Divided differences, 0101 mathematics, Error formula, Analysis

Access URL: https://core.ac.uk/display/82446606
https://www.sciencedirect.com/science/article/pii/S0021904508001640#!
https://www.sciencedirect.com/science/article/pii/S0021904508001640
https://dialnet.unirioja.es/servlet/articulo?codigo=3077845
https://www.sciencedirect.com/science/article/abs/pii/S0021904508001640
https://dblp.uni-trier.de/db/journals/jat/jat161.html#Waldron09

An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data

Authors: Nobile, F. Tempone, Raul Webster, C. G.

Source: SIAM Journal on Numerical Analysis. 46(5):2411-2442

Subject Terms: collocation techniques, PDEs with random data, differential equations, finite elements, uncertainty quantification, anisotropic sparse grids, Smolyak sparse approximation, multivariate polynomial approximation, elliptic problems, finite-elements, uncertainty, coefficients, approximations, propagation, expansions, quadrature, chaos

File Description: print

Access URL: https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-17703

A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data

Authors: NOBILE, FABIO TEMPONE R WEBSTER C.

Source: SIAM Journal on Numerical Analysis. 46:2309-2345

Subject Terms: collocation techniques, stochastic PDEs, finite elements, uncertainty quantification, sparse grids, Smolyak approximation, multivariate polynomial approximation, 0101 mathematics, 01 natural sciences

File Description: application/pdf

Access URL: http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJNAAM000046000005002309000001&idtype=cvips&gifs=yes
https://hdl.handle.net/11311/513570
https://doi.org/10.1137/060663660

Polynomial Meshes: Computation and Approximation

Authors: DE MARCHI, STEFANO PIAZZON, FEDERICO SOMMARIVA, ALVISE et al.

Contributors: DE MARCHI, STEFANO PIAZZON, FEDERICO SOMMARIVA, ALVISE et al.

Subject Terms: Multivariate Polynomial Approximation, Weakly Admissible Meshes, Discrete Extremal Sets

File Description: STAMPA

Relation: info:eu-repo/semantics/altIdentifier/isbn/978-84-617-2230-3; ispartofbook:CMMSE 2015 : Proceedings of the 15th International Conference on Mathematical Methods in Science and Engineering; volume:I-II-III-IV; firstpage:414; lastpage:425; numberofpages:12; alleditors:J. Vigo-Aguiar; https://hdl.handle.net/11577/3167966; http://cmmse.usal.es

Availability: https://hdl.handle.net/11577/3167966
http://cmmse.usal.es

A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

Authors: Ivo Babus caron Raul Tempone Fabio Nobile et al.

Contributors: Ivo Babus caron Raul Tempone Fabio Nobile et al.

Source: SIAM Journal on Numerical Analysis. 45:1005-1034

Subject Terms: uncertainty quantification, convergence rates, partial differential equations with random inputs, finite elements, stochastic collocation method, multivariate polynomial approximation, Smolyak approximation, anisotropic sparse approximation, 0101 mathematics, 01 natural sciences

File Description: application/pdf

Access URL: https://repository.kaust.edu.sa/bitstream/10754/555664/1/100786356.pdf
https://dblp.uni-trier.de/db/journals/siamnum/siamnum45.html#BabuskaNT07
http://kth.diva-portal.org/smash/record.jsf?pid=diva2:334790
https://research.kaust.edu.sa/en/publications/a-stochastic-collocation-method-for-elliptic-partial-differential-2
http://www.diva-portal.org/smash/record.jsf?pid=diva2:334790
https://dl.acm.org/doi/10.1137/050645142
https://epubs.siam.org/doi/10.1137/050645142
https://hdl.handle.net/11311/551573
https://doi.org/10.1137/050645142
https://hdl.handle.net/11311/573742
http://siamdl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SIREAD000052000002000317000001&idtype=cvips&gifs=Yes
https://doi.org/10.1137/100786356

Shape‐preserving multivariate polynomial approximation in C[−1,1]m: Shape-preserving multivariate polynomial approximation in \(C[-1,1]^m\)

Authors: Ciprian S. Gal Sorin G. Gal

Source: International Journal of Mathematics and Mathematical Sciences, Vol 2004, Iss 7, Pp 325-333 (2004)

Subject Terms: Approximation by polynomials, Approximation with constraints, QA1-939, Multidimensional problems, shape preserving approximation, 01 natural sciences, Mathematics, multivariate polynomial approximation, 0104 chemical sciences

File Description: application/xml

Access URL: http://downloads.hindawi.com/journals/ijmms/2004/934927.pdf
https://doaj.org/article/657fd60b3b9d4ece9182c1d9ec4b24d8
https://www.maths.tcd.ie/EMIS/journals/HOA/IJMMS/2004/5-8325.pdf
https://dblp.uni-trier.de/db/journals/ijmmsc/ijmmsc2004.html#GalG04
https://downloads.hindawi.com/journals/ijmms/2004/934927.pdf
https://www.hindawi.com/journals/ijmms/2004/934927/
https://eudml.org/doc/51721

The theory of multi-dimensional polynomial approximation

Authors: Moshe Dubiner

Source: Journal d'Analyse Mathématique. 67:39-116

Subject Terms: Approximation by polynomials, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), quasi-optimal metrics, Multidimensional problems, modulus of approximation, 0101 mathematics, 01 natural sciences, multivariate polynomial approximation

File Description: application/xml

Access URL: https://link.springer.com/content/pdf/10.1007/BF02787786.pdf
https://link.springer.com/article/10.1007%2FBF02787786

Polynomial Interpolation and Hyperinterpolation over General Regions: Polynomial interpolation and hyperinterpolation over general regions

Authors: Ian H. Sloan

Source: Journal of Approximation Theory. 83:238-254

Subject Terms: Mathematics(all), Numerical Analysis, Approximation by polynomials, Applied Mathematics, quadrature, 0101 mathematics, Numerical quadrature and cubature formulas, 01 natural sciences, multivariate polynomial approximation, Analysis, Approximate quadratures

File Description: application/xml

Access URL: https://zbmath.org/827935
https://doi.org/10.1006/jath.1995.1119
https://core.ac.uk/display/81969982
https://www.sciencedirect.com/science/article/pii/S0021904585711197

Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients

Authors: Fabio Nobile Raul Tempone The Pennsylvania State University CiteSeerX Archives

Contributors: Fabio Nobile Raul Tempone The Pennsylvania State University CiteSeerX Archives

Source: http://mox.polimi.it/it/progetti/pubblicazioni/quaderni/22-2008.pdf.

Subject Terms: PDEs with random data, parabolic equations, multivariate polynomial approximation, Stochastic Galerkin methods, Stochastic Collo- cation methods, sparse grids, Smolyak approximation, Point Collocation, Monte Carlo Sampling

File Description: application/pdf

Relation: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.487.242

Availability: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.487.242
http://mox.polimi.it/it/progetti/pubblicazioni/quaderni/22-2008.pdf

Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison

Authors: J. Bäck NOBILE, FABIO TAMELLINI, LORENZO et al.

Source: Lecture Notes in Computational Science and Engineering ISBN: 9783642153365

Subject Terms: Elliptic equations - Multivariate polynomial approximation - PDEs with random data - Smolyak approximation - Stochastic collocation methods - Stochastic Galerkin methods - Uncertainty quantification, 0101 mathematics, 01 natural sciences

Access URL: https://re.public.polimi.it/handle/11311/608377
https://infoscience.epfl.ch/record/176366
https://repository.kaust.edu.sa/handle/10754/575778
https://link.springer.com/chapter/10.1007%2F978-3-642-15337-2_3
https://rd.springer.com/chapter/10.1007/978-3-642-15337-2_3
http://www.icms.org.uk/downloads/uq/Nobile.pdf
http://www.springerlink.com/content/l36v035313r1gg07
https://hdl.handle.net/11311/608377
https://doi.org/10.1007/978-3-642-15337-2_3

Constructive Approximation manuscript No. (will be inserted by the editor) Power Series Kernels

Authors: Barbara Zwicknagl The Pennsylvania State University CiteSeerX Archives

Contributors: Barbara Zwicknagl The Pennsylvania State University CiteSeerX Archives

Source: http://www.mis.mpg.de/preprints/2006/preprint2006_155.pdf.

Subject Terms: multivariate polynomial approximation, Bernstein theorem, dot prod- uct kernels, reproducing kernel Hilbert spaces, error bounds, convergence orders

File Description: application/pdf

Relation: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.86.5528; http://www.mis.mpg.de/preprints/2006/preprint2006_155.pdf

Availability: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.86.5528
http://www.mis.mpg.de/preprints/2006/preprint2006_155.pdf

ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS

Authors: Lorenzo Tamellini Raul Tempone Fabio Nobile et al.

Contributors: Lorenzo Tamellini Raul Tempone Fabio Nobile et al.

Source: Mathematical Models and Methods in Applied Sciences. 22

Subject Terms: best M-terms polynomial approximation, stochastic Galerkin methods, stochastic collocation methods, sparse grids, elliptic equations, PDEs with random data, Uncertainty quantification, multivariate polynomial approximation, Smolyak approximation, 0101 mathematics, 01 natural sciences

Access URL: https://infoscience.epfl.ch/record/176370
https://www.mate.polimi.it/biblioteca/add/qmox/23-2011.pdf
https://repository.kaust.edu.sa/handle/10754/562295
https://www.worldscientific.com/doi/abs/10.1142/S0218202512500236
https://hdl.handle.net/11311/685876
https://doi.org/10.1142/S0218202512500236
http://www.worldscientific.com/doi/abs/10.1142/S0218202512500236