"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 Legendre- Gauss quadrature are respectively quite useful. If the integrand can not be expressed as f(x)/ √1-x 2 or as g(x)·(1-x) α ·(1+x) ß or as h(x) ·(1) then the Romberg method should be used.
If the interval of integration is [0,∞] or [-∞,∞], then the Laguerre-Gauss and the Hermite-Gauss methods respectively are generally quite useful.
The results of this study indicate that the quadrature formula to use in a given situation is dependent upon the interval of integration and the integrand. However, the results also indicate certain guide lines for choosing the type of quadrature formula to use in a given situation"--Abstract, page iii.
Gillett, Billy E.
Lee, Ralph E., 1921-2010
Carlile, Robert E.
Mayhan, Kenneth G.
M.S. in Computer Science
University of Missouri at Rolla
iv, 120 pages
© 1966 Edward Lee Sartore, All rights reserved.
Thesis - Open Access
Numerical analysis -- Data processing
Gaussian quadrature formulas
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Link to Catalog Record
Sartore, Edward Lee, "Comparative analysis of numerical integration techniques" (1966). Masters Theses. 2953.