Abscissas and Weights for Guassian Quadrature For N=2 to 100, and N-125, 150, 175, 200 Page: 1
iv, 88 p.View a full description of this report.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
ABSCISSAS AND WEI GHTS FOR GAUSSIAN QUADRATURE
FOR N = 2 to 100 and N = 125, 150, 175, and 200
by
Carl H. Love
The abscissas and weights for Gaussian Quadrature of order
N = 2 to 100,and N = 125, 150, 175, and 200 are given. The abscissas
are given to twenty-four places and the error is estimated to be no
more than 1 unit in the last place. The weights are given to twenty-
three places and the error is estimated to be no more than 1 unit in
the last place. Key words: Integration, Gaussian, Quadrature.
1. INTRODUCTION
The advent of high speed digital computers has made the use
of Gaussian Quadrature formulae of very high order a practical pro-
cedure. It can be programmed with a few instructions and the awkward
abscissas are easily handled by the computer. It is a familiar technique
which usually converges rapidly, and since the whole range of inte-
gration can be covered at once instead of making many subdivisions,
it will usually be very efficient.
In addition to its use in numerical integration Gaussian
Quadrature can be used in the numerical solution of integral equations
and also in the evaluation of functions that can be written as integrals.
The last four sets of very high order were computed [1I since "exact
values of these quantities are also interesting in view of certain
unsettled theoretical conjectures that have been made about distributions
of the weights and abscissas, " It was reported by Davis and
Rabinowitz [2] that there was a "brisk demand" for the sets N = 64,
80, and 96 even though they had not been published and there existed
some doubt about their accuracy.
Upcoming Pages
Here’s what’s next.
Search Inside
This report can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Report.
Love, Carl H. Abscissas and Weights for Guassian Quadrature For N=2 to 100, and N-125, 150, 175, 200, report, December 28, 1966; Washington D.C.. (https://digital.library.unt.edu/ark:/67531/metadc70465/m1/7/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.