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Physical Sciences and Mathematics
Missouri University of Science and Technology
<p>Numerical integration<br />Numerical analysis -- Data processing<br />Gaussian quadrature formulas</p>
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Comparative Analysis Of Numerical Integration Techniques, Edward Lee Sartore
Comparative Analysis Of Numerical Integration Techniques, Edward Lee Sartore
Masters Theses
"When integrating numerically, if the integrand can be expressed exactly as a polynomial of degree n, over a finite interval; then either Simpson's rule, Romberg integration, Legendre-Gauss or Jacobi-Gauss quadrature formulas provide good results. However, if the integrand can not be expressed exactly as an nth degree polynomial, then perhaps it can be expressed as a function f(x) divided by √1-x 2, or as a function g(x) times (1-x)α (l+x)ß , where α and ß are some real numbers >1, or as a function h(x) times one. If this is the case then the Chebyshev-Gauss, Jacobi-Gauss, and …