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Modifications of Newton-Cotes formulas for computation of repeated integrals and derivatives
Standard algorithms for numerical integration are defined for simple integrals. Formulas for computation of repeated integrals and derivatives for...
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A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size
In this paper we present the first known deterministic algorithm for the construction of multiple rank-1 lattices for the approximation of periodic...
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Construction of Optimal Quadrature Formulas Exact for Exponentional-trigonometric Functions by Sobolev’s Method
The paper studies Sard’s problem on construction of optimal quadrature formulas in the space W
2 ( m ,0) by Sobolev’s method. This problem consists of... -
High-order corrected trapezoidal rules for a class of singular integrals
We present a family of high-order trapezoidal rule-based quadratures for a class of singular integrals, where the integrand has a point singularity....
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Worst-case optimal approximation with increasingly flat Gaussian kernels
We study worst-case optimal approximation of positive linear functionals in reproducing kernel Hilbert spaces induced by increasingly flat Gaussian...
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Levin methods for highly oscillatory integrals with singularities
In this paper, new Levin methods are presented for calculating oscillatory integrals with algebraic and/or logarithmic singularities. To avoid...
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Bivariate Lagrange interpolation based on Chebyshev points of the second kind
We give compact formulae of the Lagrange interpolation polynomials and cubature formulae based on the common zeros of product Chebyshev polynomials...
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Nearly Optimal Nested Sensors Location for Polynomial Regression on Complex Geometries
We compute nearly optimal nested sensors configurations for global polynomial regression on domains with a complex shape, by resorting to the recent...
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A fully discrete Galerkin method for Abel-type integral equations
In this paper, we present a Galerkin method for Abel-type integral equation with a general class of kernel. Stability and quasi-optimal convergence...
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Two-Point Ostrowski’s Inequality
In this work, a general two-point Ostrowski’s formula from an analytic point of view is presented. New triangle type inequalities for...
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A Multivariate Version of Hammer’s Inequality and Its Consequences in Numerical Integration
According to Hammer’s inequality (Hammer in Math Mag 31:193–195,
1958 ), which is a refined version of the famous Hermite–Hadamard inequality, the... -
Schur-convexity and monotonicity of error of a general three-point quadrature formula
We study a general three-point quadrature formula and give necessary and sufficient conditions for this type of quadrature formula to be...
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Error estimation for quadrature by expansion in layer potential evaluation
In boundary integral methods it is often necessary to evaluate layer potentials on or close to the boundary, where the underlying integral is...
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Sobolev estimates for constructive uniform-grid FFT interpolatory approximations of spherical functions
The fast Fourier transform (FFT) based matrix-free ansatz interpolatory approximations of periodic functions are fundamental for efficient...
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Quadrature Rules for L 1-Weighted Norms of Orthogonal Polynomials
In this paper, we obtain L 1 -weighted norms of classical orthogonal polynomials (Hermite, Laguerre and Jacobi polynomials) in terms of the zeros of...