Polynomial Approximation of Anisotropic Analytic Functions of Several Variables

Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on Taylor expansions, and study their approximation by finite d...

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Vydáno v:	Constructive approximation Ročník 53; číslo 2; s. 319 - 348
Hlavní autoři:	Bonito, Andrea, DeVore, Ronald, Guignard, Diane, Jantsch, Peter, Petrova, Guergana
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.04.2021 Springer Nature B.V
Témata:	Analysis Analytic functions Approximation Budgets Mathematics Mathematics and Statistics Numerical Analysis Numerical methods Partial differential equations Polynomials 65N15 Anisotropic analyticity 41A58 41A63 Approximations and expansions 41A10 Parametric PDEs
ISSN:	0176-4276, 1432-0940
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Abstract	Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on Taylor expansions, and study their approximation by finite dimensional polynomial spaces P Λ described by lower sets Λ . Given a budget n for the dimension of P Λ , we prove that certain lower sets Λ n , with cardinality n , provide a certifiable approximation error that is in a certain sense optimal, and that these lower sets have a simple definition in terms of simplices. Our main goal is to obtain approximation results when the number of variables d is large and even infinite, and so we concentrate almost exclusively on the case d = ∞ . We also emphasize obtaining results which hold for the full range n ≥ 1 , rather than asymptotic results that only hold for n sufficiently large. In applications, one typically wants n small to comply with computational budgets.
AbstractList	Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on Taylor expansions, and study their approximation by finite dimensional polynomial spaces PΛ described by lower sets Λ. Given a budget n for the dimension of PΛ, we prove that certain lower sets Λn, with cardinality n, provide a certifiable approximation error that is in a certain sense optimal, and that these lower sets have a simple definition in terms of simplices. Our main goal is to obtain approximation results when the number of variables d is large and even infinite, and so we concentrate almost exclusively on the case d=∞. We also emphasize obtaining results which hold for the full range n≥1, rather than asymptotic results that only hold for n sufficiently large. In applications, one typically wants n small to comply with computational budgets. Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on Taylor expansions, and study their approximation by finite dimensional polynomial spaces P Λ described by lower sets Λ . Given a budget n for the dimension of P Λ , we prove that certain lower sets Λ n , with cardinality n , provide a certifiable approximation error that is in a certain sense optimal, and that these lower sets have a simple definition in terms of simplices. Our main goal is to obtain approximation results when the number of variables d is large and even infinite, and so we concentrate almost exclusively on the case d = ∞ . We also emphasize obtaining results which hold for the full range n ≥ 1 , rather than asymptotic results that only hold for n sufficiently large. In applications, one typically wants n small to comply with computational budgets.
Author	Bonito, Andrea Guignard, Diane Jantsch, Peter Petrova, Guergana DeVore, Ronald
Author_xml	– sequence: 1 givenname: Andrea surname: Bonito fullname: Bonito, Andrea organization: Department of Mathematics Texas, A&M University – sequence: 2 givenname: Ronald surname: DeVore fullname: DeVore, Ronald organization: Department of Mathematics Texas, A&M University – sequence: 3 givenname: Diane surname: Guignard fullname: Guignard, Diane organization: Department of Mathematics Texas, A&M University – sequence: 4 givenname: Peter surname: Jantsch fullname: Jantsch, Peter email: pjantsch@math.tamu.edu organization: Department of Mathematics Texas, A&M University – sequence: 5 givenname: Guergana surname: Petrova fullname: Petrova, Guergana organization: Department of Mathematics Texas, A&M University
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References	Tran, Webster, Zhang (CR20) 2017; 137 Cohen, DeVore, Schwab (CR14) 2011; 9 Griebel, Oettershagen (CR17) 2016; 207 Luca, Mukhopadhyay, Srinivas (CR18) 2010; 142 Beck, Nobile, Tamellini, Tempone (CR2) 2012; 22 Canfield, Erdös, Pomerance (CR10) 1983; 17 Cohen, DeVore (CR13) 2015; 24 Riordan (CR19) 1978 de Azevedo Pribitkin (CR16) 2009; 18 Beck, Nobile, Tamellini, Tempone (CR3) 2014; 67 Bieri, Andreev, Schwab (CR5) 2009; 31 Binev, Dahmen, DeVore (CR6) 2004; 97 CR22 Bachmayr, Cohen, Migliorati (CR1) 2017; 51 Beged-Dov (CR4) 1972; 22 Chkifa, Cohen, Schwab (CR12) 2015; 9 Cohen, Migliorati (CR15) 2018 Brenner, Scott (CR9) 2007 Chkifa, Cohen, DeVore, Schwab (CR11) 2013; 47 Yau, Zhang (CR21) 2006; 13 Binev, Dahmen, DeVore, Petrushev (CR7) 2002; 28 Bonito, DeVore, Nochetto (CR8) 2013; 51 A Cohen (9511_CR13) 2015; 24 S Yau (9511_CR21) 2006; 13 M Griebel (9511_CR17) 2016; 207 J Riordan (9511_CR19) 1978 P Binev (9511_CR7) 2002; 28 A Bonito (9511_CR8) 2013; 51 A Beged-Dov (9511_CR4) 1972; 22 M Bachmayr (9511_CR1) 2017; 51 J Beck (9511_CR3) 2014; 67 S Brenner (9511_CR9) 2007 A Cohen (9511_CR14) 2011; 9 W de Azevedo Pribitkin (9511_CR16) 2009; 18 A Chkifa (9511_CR12) 2015; 9 A Cohen (9511_CR15) 2018 M Bieri (9511_CR5) 2009; 31 E Canfield (9511_CR10) 1983; 17 H Tran (9511_CR20) 2017; 137 A Chkifa (9511_CR11) 2013; 47 9511_CR22 P Binev (9511_CR6) 2004; 97 J Beck (9511_CR2) 2012; 22 F Luca (9511_CR18) 2010; 142
References_xml	– volume: 31 start-page: 4281 issue: 6 year: 2009 end-page: 4304 ident: CR5 article-title: Sparse tensor discretizations of elliptic SPDEs publication-title: SIAM J. Sci. Comput. doi: 10.1137/090749256 – volume: 9 start-page: 400 issue: 2 year: 2015 end-page: 428 ident: CR12 article-title: Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs publication-title: J. Math. Pures Appl. doi: 10.1016/j.matpur.2014.04.009 – start-page: 233 year: 2018 end-page: 282 ident: CR15 article-title: Multivariate approximation in downward closed polynomial spaces publication-title: In: Contemporary Computational Mathematics—A Celebration of the 80th Birthday of Ian Sloan, Vols 1 and 2 doi: 10.1007/978-3-319-72456-0_12 – ident: CR22 – volume: 137 start-page: 451 issue: 2 year: 2017 end-page: 493 ident: CR20 article-title: Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients publication-title: Numer. Math. doi: 10.1007/s00211-017-0878-6 – volume: 207 start-page: 348 year: 2016 end-page: 379 ident: CR17 article-title: On tensor product approximation of analytic functions publication-title: J. Approx. Theory doi: 10.1016/j.jat.2016.02.006 – volume: 17 start-page: 1 issue: 1 year: 1983 end-page: 28 ident: CR10 article-title: On a problem of Oppenheim concerning “factorisatio numerorum” publication-title: J. Number Theory doi: 10.1016/0022-314X(83)90002-1 – year: 1978 ident: CR19 publication-title: An Introduction to Combinatorial Analysis – volume: 28 start-page: 391 issue: 4 year: 2002 end-page: 416 ident: CR7 article-title: Approximation classes for adaptive methods publication-title: Serdica Math. J. – volume: 22 start-page: 106 issue: 1 year: 1972 end-page: 108 ident: CR4 article-title: Lower and upper bounds for the number of lattice points in a simplex publication-title: SIAM J. Appl. Math. doi: 10.1137/0122012 – volume: 18 start-page: 113 issue: 1 year: 2009 end-page: 119 ident: CR16 article-title: Simple upper bounds for partition functions publication-title: Ramanujan J. doi: 10.1007/s11139-007-9022-z – volume: 47 start-page: 253 issue: 1 year: 2013 end-page: 280 ident: CR11 article-title: Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs publication-title: ESAIM: Math. Modell. Numer. Anal. doi: 10.1051/m2an/2012027 – volume: 9 start-page: 11 issue: 1 year: 2011 end-page: 47 ident: CR14 article-title: Analytic regularity and polynomial approximation of parametric stochastic elliptic PDEs publication-title: Anal. Appl. doi: 10.1142/S0219530511001728 – volume: 51 start-page: 321 issue: 1 year: 2017 end-page: 339 ident: CR1 article-title: Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients publication-title: ESAIM: Math. Modell. Numer. Anal. doi: 10.1051/m2an/2016045 – volume: 22 start-page: 1250023 issue: 9 year: 2012 ident: CR2 article-title: On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202512500236 – year: 2007 ident: CR9 publication-title: The Mathematical Theory of Finite Element Methods – volume: 24 start-page: 1 year: 2015 end-page: 159 ident: CR13 article-title: Approximation of high-dimensional parametric PDEs publication-title: Acta Numer. doi: 10.1017/S0962492915000033 – volume: 67 start-page: 732 issue: 4 year: 2014 end-page: 751 ident: CR3 article-title: Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2013.03.004 – volume: 97 start-page: 219 issue: 2 year: 2004 end-page: 268 ident: CR6 article-title: Adaptive finite element methods with convergence rates publication-title: Numerische Mathematik doi: 10.1007/s00211-003-0492-7 – volume: 13 start-page: 911 issue: 5 year: 2006 end-page: 921 ident: CR21 article-title: An upper estimate of integral points in real simplices with an application to singularity theory publication-title: Math. Res. Lett. doi: 10.4310/MRL.2006.v13.n6.a6 – volume: 142 start-page: 41 year: 2010 end-page: 50 ident: CR18 article-title: Some results on Oppenheim’s “Factorisatio Numerorum” function publication-title: Acta Arithmetica doi: 10.4064/aa142-1-3 – volume: 51 start-page: 3106 issue: 6 year: 2013 end-page: 3134 ident: CR8 article-title: Adaptive finite element methods for elliptic problems with discontinuous coefficients publication-title: SIAM J. Numer. Anal. doi: 10.1137/130905757 – volume: 18 start-page: 113 issue: 1 year: 2009 ident: 9511_CR16 publication-title: Ramanujan J. doi: 10.1007/s11139-007-9022-z – volume: 47 start-page: 253 issue: 1 year: 2013 ident: 9511_CR11 publication-title: ESAIM: Math. Modell. Numer. Anal. doi: 10.1051/m2an/2012027 – volume: 13 start-page: 911 issue: 5 year: 2006 ident: 9511_CR21 publication-title: Math. Res. Lett. doi: 10.4310/MRL.2006.v13.n6.a6 – volume: 67 start-page: 732 issue: 4 year: 2014 ident: 9511_CR3 publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2013.03.004 – volume-title: An Introduction to Combinatorial Analysis year: 1978 ident: 9511_CR19 – volume: 22 start-page: 106 issue: 1 year: 1972 ident: 9511_CR4 publication-title: SIAM J. Appl. Math. doi: 10.1137/0122012 – volume: 9 start-page: 11 issue: 1 year: 2011 ident: 9511_CR14 publication-title: Anal. Appl. doi: 10.1142/S0219530511001728 – volume: 9 start-page: 400 issue: 2 year: 2015 ident: 9511_CR12 publication-title: J. Math. Pures Appl. doi: 10.1016/j.matpur.2014.04.009 – start-page: 233 volume-title: In: Contemporary Computational Mathematics—A Celebration of the 80th Birthday of Ian Sloan, Vols 1 and 2 year: 2018 ident: 9511_CR15 doi: 10.1007/978-3-319-72456-0_12 – ident: 9511_CR22 doi: 10.3929/ethz-b-000340651 – volume: 31 start-page: 4281 issue: 6 year: 2009 ident: 9511_CR5 publication-title: SIAM J. Sci. Comput. doi: 10.1137/090749256 – volume: 97 start-page: 219 issue: 2 year: 2004 ident: 9511_CR6 publication-title: Numerische Mathematik doi: 10.1007/s00211-003-0492-7 – volume: 17 start-page: 1 issue: 1 year: 1983 ident: 9511_CR10 publication-title: J. Number Theory doi: 10.1016/0022-314X(83)90002-1 – volume: 51 start-page: 321 issue: 1 year: 2017 ident: 9511_CR1 publication-title: ESAIM: Math. Modell. Numer. Anal. doi: 10.1051/m2an/2016045 – volume-title: The Mathematical Theory of Finite Element Methods year: 2007 ident: 9511_CR9 – volume: 51 start-page: 3106 issue: 6 year: 2013 ident: 9511_CR8 publication-title: SIAM J. Numer. Anal. doi: 10.1137/130905757 – volume: 24 start-page: 1 year: 2015 ident: 9511_CR13 publication-title: Acta Numer. doi: 10.1017/S0962492915000033 – volume: 207 start-page: 348 year: 2016 ident: 9511_CR17 publication-title: J. Approx. Theory doi: 10.1016/j.jat.2016.02.006 – volume: 22 start-page: 1250023 issue: 9 year: 2012 ident: 9511_CR2 publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202512500236 – volume: 137 start-page: 451 issue: 2 year: 2017 ident: 9511_CR20 publication-title: Numer. Math. doi: 10.1007/s00211-017-0878-6 – volume: 28 start-page: 391 issue: 4 year: 2002 ident: 9511_CR7 publication-title: Serdica Math. J. – volume: 142 start-page: 41 year: 2010 ident: 9511_CR18 publication-title: Acta Arithmetica doi: 10.4064/aa142-1-3
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SubjectTerms	Analysis Analytic functions Approximation Budgets Mathematics Mathematics and Statistics Numerical Analysis Numerical methods Partial differential equations Polynomials
Title	Polynomial Approximation of Anisotropic Analytic Functions of Several Variables
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