A new type of Chebyshev quadrature

Authors:
R. E. Barnhill, J. E. Dennis and G. M. Nielson

Journal:
Math. Comp. **23** (1969), 437-441

MSC:
Primary 65.55

MathSciNet review:
0242367

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Abstract: A Chebyshev quadrature is of the form

It is usually desirable that the nodes

be in the interval of integration and that the quadrature be exact for as many monomials as possible (i.e., the first

monomials). For

and

, such a choice of nodes is possible, but for

and

, the nodes are complex. In this note, the idea used is that the

-norm of the deviations of the first

monomials from their moments be a minimum. Numerical calculations are carried out for

, and

and one interesting feature of the numerical results is that a ``multiple'' node at the origin is required. The above idea is then generalized to a minimization of the

-norm of the deviations of the first

monomials,

, including

, and corresponding numerical results are presented.

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*J. Math. Anal. Appl.*, v. 15, 1966, pp. 243-252. MR **34** #5273. MR **0205445 (34:5273)**
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DOI:
https://doi.org/10.1090/S0025-5718-1969-0242367-4

Article copyright:
© Copyright 1969
American Mathematical Society