NDLI: A class of numerical integration rules with first order derivatives

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Volume 31, Issue 4, Oct. 1996

Volume 31, Issue 3, July 1996

Volume 31, Issue 2, April 1996

Note on local methods of univariate interpolation

For unknown-but-bounded errors, interval estimates are often better than averaging

An example of error propagation reinterpreted as subtractive cancellation—revisited

Remark on “An example of error propagation reinterpreted as subtractive cancellation” by J. A. Delaney (SIGNUM Newsletter 1/96)

A class of numerical integration rules with first order derivatives

Volume 31, Issue 1, Jan. 1996

A class of numerical integration rules with first order derivatives

Content Provider	ACM Digital Library
Author	Al-Alaoui, Mohamad Adnan
Abstract	A novel approach to deriving a family of quadrature formulae is presented. The first member of the new family is the corrected trapezoidal rule. The second member, a two-segment rule, is obtained by interpolating the corrected trapezoidal rule and the Simpson one-third rule. The third member, a three-segment rule, is obtained by interpolating the corrected trapezoidal rule and the Simpson three-eights rule. The fourth member, a four-segment rule is obtained by interpolating the two-segment rule with the Boole rule. The process can be carried on to generate a whole class of integration rules by interpolating the proposed rules appropriately with the Newton-Cotes rules to cancel out an additional term in the Euler-MacLaurin error formula. The resulting rules integrate correctly polynomials of degrees less or equal to n+3 if n is even and n+2 if n is odd, where n is the number of segments of the single application rules. The proposed rules have excellent round-off properties, close to those of the trapezoidal rule. Members of the new family obtain with two additional functional evaluations the same order of errors as those obtained by doubling the number of segments in applying the Romberg integration to Newton-Cotes rules. Members of the proposed family are shown to be viable alternatives to Gaussian quadrature.
Starting Page	25
Ending Page	44
Page Count	20
File Format	PDF
ISSN	01635778
DOI	10.1145/230922.230930
Journal	ACM SIGNUM Newsletter (SGNM)
Volume Number	31
Issue Number	2
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1990-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article

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