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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2018 • Question 3

Question

Math 6610 • Analysis of Numerical Methods I Spring 2018 • Question 3

Quadrature

Consider the quadrature rule \[ \int _{-1}^{1} f(x)\,dx \approx w_{-1}f(-1)+w_0f(0)+w_1f(1)+w_0'f'(0). \] Compute weights \(w_{-1}\), \(w_0\), \(w_1\), and \(w_0'\) such that this quadrature rule is exact for polynomials up to degree 3.

Raw LaTeX

{Quadrature}

Consider the quadrature rule
\[
  \int_{-1}^{1} f(x)\,dx
  \approx
  w_{-1}f(-1)+w_0f(0)+w_1f(1)+w_0'f'(0).
\]
Compute weights \(w_{-1}\), \(w_0\), \(w_1\), and \(w_0'\) such that this quadrature
rule is exact for polynomials up to degree 3.

Topic Tags

Linear Programming and Optimization Numerical Quadrature Polynomial Interpolation and Error Formulas Quadrature Rules