Chebyshev-type Quadratures for Doubling Weights
arXiv:1507.015053 citations
AI Analysis
Provides theoretical bounds for numerical integration with equal weights, advancing a classical problem in approximation theory.
The paper extends Kane's method to derive tight bounds on the minimal number of nodes for Chebyshev-type quadratures (equal-weight formulas) for doubling weight functions, building on Bernstein's 1937 work.
A Chebyshev-type quadrature for a given weight function is a quadrature formula with equal weights. In this work we show that a method presented by Kane may be used to produce tight bounds for the minimal number of nodes required in Chebyshev-type quadratures for doubling weight functions. This extends a long line of research on Chebyshev-type quadratures starting with the 1937 work of Bernstein.