Optimal quadrature formulas using generalized inverses. I. General theory and minimum variance formulas

Author:
C. S. Duris

Journal:
Math. Comp. **25** (1971), 495-504

MSC:
Primary 65D30

DOI:
https://doi.org/10.1090/S0025-5718-1971-0295567-0

MathSciNet review:
0295567

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Abstract: This paper is the first of two papers concerning the derivation of optimal quadrature formulas. In Part I, we develop results concerning generalized inverses and use these results to derive some minimum variance quadrature formulas. The formulas are obtained by inverting appropriate systems of numerical differentiation formulas. The second paper, Part II, will use the same results concerning generalized inverses to derive Sard ``best'' quadrature formulas.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1971-0295567-0

Keywords:
Quadrature formulas,
generalized inverses,
minimum variance formulas inverting numerical differentiation formulas

Article copyright:
© Copyright 1971
American Mathematical Society