How sharp are error bounds? -- Lower bounds on quadrature worst-case errors for analytic functions --
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Publication:6633129
DOI10.1137/24m1634163MaRDI QIDQ6633129
Yoshihito Kazashi, Ken'ichiro Tanaka, Takashi Goda
Publication date: 5 November 2024
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
numerical integrationGauss quadraturequadrature formulaanalytic functionsworst-case errortrapezoidal ruleClenshaw-Curtis
Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Banach spaces of continuous, differentiable or analytic functions (46E15) Numerical integration (65D30) Real-analytic functions (26E05)
Cites Work
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- New lower bound estimates for quadratures of bounded analytic functions
- Asymptotics on Laguerre or Hermite polynomial expansions and their applications in Gauss quadrature
- High dimensional integration of kinks and jumps -- smoothing by preintegration
- A note on the optimal quadrature in \(H^ p\)
- Tractability of multivariate problems. Volume I: Linear information
- Optimal quadrature of Hp functions
- Double exponential formulas for numerical integration
- Quadrature formulae for \(H^p\) functions
- Optimal integration of Lipschitz functions with a Gaussian weight
- Optimality of the double exponential formula -- functional analysis approach
- Gaussian versus optimal integration of analytic functions
- Algorithms for the computation of the matrix logarithm based on the double exponential formula
- High-order quadrature on multi-component domains implicitly defined by multivariate polynomials
- Fast CBC construction of randomly shifted lattice rules achieving \(\mathcal{O}(n^{- 1 + \delta})\) convergence for unbounded integrands over \(\mathbb{R}^s\) in weighted spaces with POD weights
- Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems
- Proof techniques in quasi-Monte Carlo theory
- On the approximate calculation of multiple integrals
- Numerical integration of analytic functions
- On the power of adaption
- The Exponentially Convergent Trapezoidal Rule
- Convergence Properties of Gaussian Quadrature Formulae
- Construction of Approximation Formulas for Analytic Functions by Mathematical Optimization
- Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
- Potential Theoretic Approach to Design of Accurate Numerical Integration Formulas in Weighted Hardy Spaces
- Uncertainty Quantification for Low-Frequency, Time-Harmonic Maxwell Equations with Stochastic Conductivity Models
- On the Optimal Order of Integration in Hermite Spaces with Finite Smoothness
- Potential theoretic approach to design of accurate formulas for function approximation in symmetric weighted Hardy spaces
- Exactness of Quadrature Formulas
- Error bounds of potential theoretic numerical integration formulas in weighted Hardy spaces
- Design of accurate formulas for approximating functions in weighted Hardy spaces by discrete energy minimization
- On The Use of Conformal Maps for the Acceleration of Convergence of the Trapezoidal Rule and Sinc Numerical Methods
- Dimension-Adaptive Sparse Grid Quadrature for Integrals with Boundary Singularities
- Sparse grids
- High-dimensional integration: The quasi-Monte Carlo way
- On the optimal speed of integrating analytic functions
- Integration Formulae Based on the Trapezoidal Formula
- Randomizing the trapezoidal rule gives the optimal RMSE rate in Gaussian Sobolev spaces
- Suboptimality of Gauss–Hermite Quadrature and Optimality of the Trapezoidal Rule for Functions with Finite Smoothness
- Convergence analysis of approximation formulas for analytic functions via duality for potential energy minimization
- Algorithm 1040: the Sparse Grids Matlab Kit -- a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification
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