Numerical integration using sparse grids
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Summary
The usage of extended Gauss (Patterson) quadrature formulas as the one‐dimensional basis of the construction is suggested and their superiority in comparison to previously used sparse grid approaches based on the trapezoidal, Clenshaw–Curtis and Gauss rules is shown.
- Type
- article
- Published
- 2004-01-01
- Cited by
- 1,009
- References
- 66
- OpenAlex
- https://openalex.org/W1646309082
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:778918
Keywords
Sparse grid, Gauss–Kronrod quadrature formula, Mathematics, Quadrature (astronomy), Numerical integration
References
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- An adaptive algorithm for numerical integration over the n-cube
- An estimate of the complexity of the approximate solution of fredholm equations of the second kind with differentiable kernels
- A method for numerical integration on an automatic computer
- Neural networks and approximation theory
- Computing Discrepancies of Smolyak Quadrature Rules
- Lattice Methods for Multiple Integration
- High dimensional integration of smooth functions over cubes
- The optimum addition of points to quadrature formulae.
- An adaptive algorithm for numerical integration over an n-dimensional rectangular region
- Calculation of Gauss quadratures with multiple free and fixed knots
- Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems
- Perspectives on information-based complexity
- Stieltjes Polynomials and Related Quadrature Rules
- d-Variate Boolean interpolation
- The Combination Technique for the Sparse Grid Solution of PDE's on Multiprocessor Machines
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- Résolution de modèles d'évaluation de produits dérivés financiers sur des architectures de grilles informatiques
- Méthodes de Galerkin stochastiques adaptatives pour la propagation d'incertitudes paramétriques dans les modèles hyperboliques
- Sampling and Cubature on Sparse Grids Based on a B-spline Quasi-Interpolation
- COMPUTATIONAL STRATEGIES FOR DATA-DRIVEN MODELING OF STOCHASTIC SYSTEMS
- Basket Option Pricing on Sparse Grids Using Fast Fourier Transforms
- Covering Pascal's Triangle on a Budget: Accuracy, Precision and Eciency in Sparse Grids
- Hybrid Solution of Stochastic Optimal Control Problems Using Gauss Pseudospectral Method and Generalized Polynomial Chaos Algorithms
- Fast Parameter-Space Sweep of Wideband Electromagnetic Systems Using Bt-pod
- A generic reliability analysis and design framework with random parameter, field, and process variables
- Classification and Overview of Meshfree Methods
- Technical Report: Scalable Parallel Algorithms for High Dimensional Numerical Integration
- Estimation, Decision and Applications to Target Tracking
- Few group cross section representation based on sparse grid methods
- Technical Report: Toward a Scalable Algorithm to Compute High-Dimensional Integrals of Arbitrary Functions
- Efficient algorithms for mixed aleatory-epistemic uncertainty quantification with application to radiation-hardened electronics. Part I, algorithms and benchmark results.
- An Approach for the Adaptive Solution of Optimization Problems Governed by Partial Differential Equations with Uncertain Coefficients
- IUTAM Symposium on "Dynamical Analysis of Multibody Systems with Design Uncertainties" Sensitivity computation for uncertain dynamical systems using high-dimensional model representation and hierarchical grids
- COMPUTATIONAL TECHNIQUES FOR UNCERTAINTY MODELING AND STOCHASTIC OPTIMIZATION OF MATERIAL SYSTEMS
- Uncertainty quantification in reactor physics using adjoint/perturbation techniques and adaptive spectral methods
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