Methods of Convergence Improvement for Some Improper Integrals

In the numerical integration of an improper
integral of the first kind, it is customary to 
truncate the integral when the change yielded by the last
iteration is less than some predetermined constant. 
The efficiency of such integration schemes can often
be improved by use of recent advances in the theory 
of nonlinear transformations; however, for several important
integrals, e.g. integrals whose integrands 
are rational polynomials, these transformations fail
to yield much improvement.  In this paper, several 
methods of convergence improvement are developed which greatly
improve convergence of some improper integrals, 
including the integrals of rational polynomials.

CACM July, 1968

McWilliams, G. V.
Thompson, R. W.

approximation, nonlinear, improper integral, convergence
improvement, numerical integration, rational 
polynomials, truncation

3.15 5.13 5.16 5.19

CA680707 JB February 22, 1978  11:58 AM

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