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A Method of Computing Limit Values
SIAM Journal on Numerical Analysis
Vol. 10, No. 6 (Dec., 1973), pp. 1080-1090
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2156205
Page Count: 11
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The general idea of this paper is that a limit value always can be written as the sum of an infinite series. The latter is recast in the form of a Stieltjes integral, which can be treated numerically by means of mechanical quadrature rules. This procedure is used for a unified and effective treatment of various problems as the summation of slowly convergent series and double series, as well as integrals over infinite ranges. The results of this paper are based on the methods presented in S.-A. Gustafson  for the summation of certain series. By proper selection of weight functions rapid convergence and accurate results are often obtained, which is demonstrated on several examples. Realistic and strict bounds for the influence of computational errors are easily constructed as well.
SIAM Journal on Numerical Analysis © 1973 Society for Industrial and Applied Mathematics