CALCULATION OF GAUSS QUADRATURE RULES.
STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE
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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 gt 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 ft sub i. Hopefully, the quadrature rule w sub j, t sub j subscript j 1, superscript N corresponding to the weight function omegat 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 omegat, and b the moments of the weight function are known or can be calculated. Author
- Theoretical Mathematics