NDLI: A Family of Quadrature Formulas Which Achieve High Accuracy in Composite Rules

Content Provider	ACM Digital Library
Author	Ralston, A.
Copyright Year	1959
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.
Starting Page	384
Ending Page	394
Page Count	11
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/320986.320993
Journal	Journal of the ACM (JACM)
Volume Number	6
Issue Number	3
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1959-07-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

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