Newton–Cotes formulas

Target entity: Newton–Cotes formulas
Context triple: [Simpson's rule, specialCaseOf, Newton–Cotes formulas]

• A. Gaussian quadrature rules
  Gaussian quadrature rules are numerical integration methods that approximate definite integrals by optimally choosing evaluation points and weights to achieve exactness for polynomials up to a high degree.
• B. Simpson's rule
  Simpson's rule is a numerical integration technique that approximates the area under a curve by fitting parabolas through groups of data points.
• C. Euler–Maclaurin summation formula
  The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
• D. Birkhoff interpolation
  Birkhoff interpolation is a generalized form of polynomial interpolation that allows prescribing function and derivative values at selected points, not necessarily in a consecutive or complete pattern.
• E. Runge–Kutta methods
  Runge–Kutta methods are a family of iterative techniques for numerically solving ordinary differential equations with higher accuracy than simple one-step schemes.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Newton–Cotes formulas
Target entity description: Newton–Cotes formulas are a family of numerical integration methods that approximate definite integrals by interpolating the integrand with equally spaced polynomial points.

• A. Gaussian quadrature rules
  Gaussian quadrature rules are numerical integration methods that approximate definite integrals by optimally choosing evaluation points and weights to achieve exactness for polynomials up to a high degree.
• B. Simpson's rule
  Simpson's rule is a numerical integration technique that approximates the area under a curve by fitting parabolas through groups of data points.
• C. Euler–Maclaurin summation formula
  The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
• D. Birkhoff interpolation
  Birkhoff interpolation is a generalized form of polynomial interpolation that allows prescribing function and derivative values at selected points, not necessarily in a consecutive or complete pattern.
• E. Runge–Kutta methods
  Runge–Kutta methods are a family of iterative techniques for numerically solving ordinary differential equations with higher accuracy than simple one-step schemes.
• F. None of above. chosen