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 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.

Committee Member(s)

Lee, Ralph E., 1921-2010
Carlile, Robert E.
Mayhan, Kenneth G.


Computer Science

Degree Name

M.S. in Computer Science


University of Missouri at Rolla

Publication Date



iv, 120 pages

Note about bibliography

Includes bibliographical references (pages 118-119).


© 1966 Edward Lee Sartore, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Numerical integration
Numerical analysis -- Data processing
Gaussian quadrature formulas

Thesis Number

T 1955

Print OCLC #


Electronic OCLC #