Lower bound for quantum integration error on anisotropic Sobolev classes

DOI10.1007/s10114-010-7546-4zbMath1190.81031OpenAlexW2167332533MaRDI QIDQ966549

Pei Xin Ye

Publication date: 23 April 2010

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-010-7546-4

zbMATH Keywords

\(n\)-th minimal query erroranisotropic Sobolev classesHölder-Nikolskii classesquantum integration

Mathematics Subject Classification ID

Quantum computation (81P68) Lipschitz (Hölder) classes (26A16) Multidimensional problems (41A63) Algorithms for approximation of functions (65D15) Complexity and performance of numerical algorithms (65Y20)

Cites Work

• The quantum query complexity of elliptic PDE
• Quantum integration in Sobolev classes
• Lower bounds for centered and wrap-around \(L_2\)-discrepancies and construction of uniform designs by threshold accepting.
• Quantum summation with an application to integration.
• Optimal integration error on anisotropic classes for restricted Monte Carlo and quantum algorithms
• Quantum complexity of integration
• Nonlinear anisotropic boundary value problems -- regularity results and multiscale discretizations
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