Accession Number : AD0661217
Title : CALCULATION OF GAUSS QUADRATURE RULES.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE
Personal Author(s) : Golub,Gene H. ; Welsch,John H.
Report Date : 03 NOV 1967
Pagination or Media Count : 31
Abstract : Most numerical integration techniques consist of approximating the integrand by a polynomial in a region or regions and then integrating the polynomial exactly. Often a complicated integrand can be factored into a non-negative 'weight' function and another function better approximated by a polynomial, thus the integral from a to b of (g(t) dt) = the integral from a to b of (omega (t) f (t) dt) which approximately equals summation, i =1 to i = N, of (w sub i f(t sub i)). Hopefully, the quadrature rule (w sub j, t sub j) subscript j = 1, superscript N corresponding to the weight function omega(t) is available in tabulated form, but more likely it is not. We present here two algorithms for generating the Gaussian quadrature rule defined by the weight function when: (a) the three term recurrence relation is known for the orthogonal polynomials generated by omega(t), and (b) the moments of the weight function are known or can be calculated. (Author)
Descriptors : (*NUMERICAL ANALYSIS, *NUMERICAL INTEGRATION), POLYNOMIALS, ALGORITHMS, THEOREMS, FUNCTIONS(MATHEMATICS), MATRICES(MATHEMATICS)
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE