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Author Ralston, A.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1959
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract A class of quadrature formulas is derived which achieve higher accuracy in composite rules (i.e., where the interval of integration is broken up into a number of subintervals) than analogous Newton-Cotes or Gaussian formulas. The cost of this higher accuracy is the computation of one or two more ordinates over the whole interval of integration.The high accuracy is obtained by using Gaussian techniques in the interior of each subinterval and by using the endpoints of each subinterval as abscissas with weights of equal magnitude and opposite sign. In this way when the subintervals are put together only the endpoints of the whole interval of integration remain. It is proved that the abscissas are all real and interior to the subinterval and that the weights corresponding to the interior abscissas are positive.Since the abscissas are not equally spaced, the method is not suited to tabular functions but rather to analytically given functions. The roundoff properties of the formulas are discussed and are shown to be quite good.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1959-07-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 6
Issue Number 3
Page Count 11
Starting Page 384
Ending Page 394

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Source: ACM Digital Library