On the Complexity of Parametric ODEs and Related Problems

DOI10.1007/978-3-319-72456-0_26zbMath1405.65010OpenAlexW2804486446MaRDI QIDQ4611817

Stefan Heinrich

Publication date: 22 January 2019

Published in: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-72456-0_26

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Complexity and performance of numerical algorithms (65Y20) Complexity classes (hierarchies, relations among complexity classes, etc.) (68Q15) Numerical integration (65D30)

Cites Work

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• Sparse adaptive approximation of high dimensional parametric initial value problems
• On the randomized solution of initial value problems
• The randomized complexity of indefinite integration
• How to increase the order to get minimal-error algorithms for systems of ODE
• Randomized and quantum algorithms yield a speed-up for initial-value problems
• Almost optimal solution of initial-value problems by randomized and quantum algorithms
• Approximation theory in tensor product spaces
• Deterministic and stochastic error bounds in numerical analysis
• Monte Carlo complexity of parametric integration
• Complexity of parametric initial value problems for systems of odes
• Complexity of parametric initial value problems in Banach spaces
• Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients
• The randomized complexity of initial value problems
• Monte Carlo approximation of weakly singular integral operators
• The randomized information complexity of elliptic PDE
• Multilevel Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations
• Complexity of Banach Space Valued and Parametric Integration
• ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
• Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients
• On the calculation of definite integrals dependent on a parameter by the monte carlo method