Potential Theoretic Approach to Design of Accurate Numerical Integration Formulas in Weighted Hardy Spaces

DOI10.1007/978-3-319-59912-0_17zbMath1385.65025OpenAlexW2736794932MaRDI QIDQ4609811

Ken'ichiro Tanaka, Masaaki Sugihara, Tomoaki Okayama

Publication date: 26 March 2018

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-59912-0_17

zbMATH Keywords

algorithmnumerical integrationnumerical examplespotential theorydouble-exponential transformationweighted Hardy spaceGreen potential

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items

Error bounds of potential theoretic numerical integration formulas in weighted Hardy spaces ⋮ Construction of Approximation Formulas for Analytic Functions by Mathematical Optimization

Uses Software

• Sinc-Pack

Cites Work

• Optimal quadrature of \(H^p\) functions
• A note on the optimal quadrature in \(H^ p\)
• Function classes for double exponential integration formulas
• Double exponential formulas for numerical integration
• Optimality of the double exponential formula -- functional analysis approach
• Discovery of the double exponential transformation and its developments
• Numerical integration of analytic functions
• Quadrature formulas obtained by variable transformation
• The Exponentially Convergent Trapezoidal Rule
• The Tanh Rule for Numerical Integration
• Potential theoretic approach to design of accurate formulas for function approximation in symmetric weighted Hardy spaces
• Near optimality of the sinc approximation
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