Numerical analysis and orthogonal polynomials

摘要

Two topics of general interest are investigated. First an iterative improvement algorithm is given to reduce the accumulation of truncation errors which may occur when recursion formulae are utilized. Then some properties of orthogonal polynomials are derived that allow a successful construction of Gaussian type integration formulae employing the improvement algorithm. As special examples integrals of the ∫baexp(-x2)f(x)dx and ∫baexp(-|x|)f(x)dx are considered, where a and/o r b may be infinite.