Simple Cubature Formulas with High Polynomial Exactness
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- Type
- article
- Published
- 1999-12-01
- Cited by
- 293
- References
- 29
- OpenAlex
- https://openalex.org/W2103455761
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:123177402
Keywords
Mathematics, Simple (philosophy), Tensor product, Polynomial, Dimension (graph theory)
References
- Product-integration with the Clenshaw-Curtis and related points
- Implementing Clenshaw-Curtis quadrature, I methodology and experience
- APPROXIMATE RECOVERY OF PERIODIC FUNCTIONS OF SEVERAL VARIABLES
- Computing Discrepancies of Smolyak Quadrature Rules
- Limits on the number of function evaluations required by certain high-dimensional integration rules of hypercubic symmetry
- High dimensional integration of smooth functions over cubes
- An imbedded family of cubature formulae for n -dimensional product regions
- Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems
- Cubature Rules of Prescribed Merit
- Boolean methods for double integration
- Symmetric Integration Rules for Hypercubes III. Construction of Integration Rules Using Null Rules
- Hyperbolic cross designs for approximation of random fields
- On an interpolatory method for high dimensional integration
- A Construction of Nonnegative Approximate Quadratures
- Multidimensional Quadrature Algorithms at Higher Degree and/or Dimension
- Fully symmetric interpolatory rules for multiple integrals
- Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree
- Average Case Complexity of Multivariate Integration for Smooth Functions
- Construction of fully symmetric numerical integration formulas of fully symmetric numerical integration formulas
- Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight
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- Novel Computational Methods for Solving High- Dimensional Random Eigenvalue Problems
- Quantification of Uncertainty in Flow Simulations Using Probabilistic Methods
- An Approach for the Adaptive Solution of Optimization Problems Governed by Partial Differential Equations with Uncertain Coefficients
- Statistical Analysis for On-Chip Power Grid Networks and Interconnects Considering Process Variation
- Sensitivity and Uncertainty Analysis of Coupled Reactor Physics Problems: Method Development for Multi-Physics in Reactors
- Variance-based global sensitivity analysis for multiple scenarios and models with implementation using sparse grid collocation
- Sparse Grid Quadrature in High Dimensions with Applications in Finance and Insurance
- Solving PDEs with random data by stochastic collocation
- Mathematical and numerical analysis of the resistive magnetohydrodynamics system with self-generated magnetic field terms
- Optimisation robuste et application à la reconstruction du réseau artériel humain
- Accelerating Bayesian Inference in Computationally Expensive Computer Models Using Local and Global Approximations
- Fast calculation of coefficients in the Smolyak algorithm
- UNCERTAINTY QUANTIFICATION OF THE GEM CHALLENGE MAGNETIC RECONNECTION PROBLEM USING THE MULTILEVEL MONTE CARLO METHOD
- Tractability of Multivariate Problems
- Estimation with Numerical Integration on Sparse Grids
- Adaptive Discontinuous Galerkin Method for Response-Excitation PDF Equations
- Solving the Schroedinger equation using Smolyak interpolants.
- Stochastic design optimization: Application to reacting flows
- Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids
- Uncertainty propagation in CFD using polynomial chaos decomposition
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