A Randomized Tensor Quadrature Method for High Dimensional Polynomial Approximation

DOI10.1137/16M1081695zbMath1373.65012MaRDI QIDQ5357965

Yeonjong Shin, Kailiang Wu, Dongbin Xiu

Publication date: 18 September 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

convergenceiterative algorithmnumerical exampleapproximation theoryorthogonal polynomialmultivariate functionsrandomized Kaczmarz algorithmtensor Gauss quadrature

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Approximation by polynomials (41A10) Algorithms for approximation of functions (65D15) Numerical quadrature and cubature formulas (65D32)

Related Items (5)

Sequential function approximation with noisy data ⋮ Sequential function approximation on arbitrarily distributed point sets ⋮ Numerical aspects for approximating governing equations using data ⋮ Sequential approximation of functions in Sobolev spaces using random samples ⋮ Generating Nested Quadrature Rules with Positive Weights based on Arbitrary Sample Sets

Uses Software

• TESTPACK

Cites Work

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• Convergence acceleration of Kaczmarz's method
• Acceleration of randomized Kaczmarz method via the Johnson-Lindenstrauss lemma
• Randomized Kaczmarz solver for noisy linear systems
• A randomized Kaczmarz algorithm with exponential convergence
• Almost sure convergence of the Kaczmarz algorithm with random measurements
• High dimensional polynomial interpolation on sparse grids
• Weighted discrete least-squares polynomial approximation using randomized quadratures
• Randomized Extended Kaczmarz for Solving Least Squares
• An accelerated randomized Kaczmarz algorithm
• A Randomized Algorithm for Multivariate Function Approximation
• Sparse grids

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