Volume 19, Issue 5
An Extremal Approach to Birkhoff Quadrature Formulas

Ying Guang Shi

J. Comp. Math., 19 (2001), pp. 459-466

Published online: 2001-10

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  • Abstract

As we know, a solution of an extremal problem with Hermite interpolation constraints is a system of nodes of corresponding Gaussian Hermite quadrature formula (the so-called Jacobi approach). But this conclusion is violated for a Birkhoff quadrature formula. In this paper an extremal problem with Birkhoff interpolation constraints is discussed, from which a large class of Birkhoff quadrature formulas may be derived.

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An extremal approach Birkhoff quadrature formulas

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@Article{JCM-19-459, author = {}, title = {An Extremal Approach to Birkhoff Quadrature Formulas}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {5}, pages = {459--466}, abstract = { As we know, a solution of an extremal problem with Hermite interpolation constraints is a system of nodes of corresponding Gaussian Hermite quadrature formula (the so-called Jacobi approach). But this conclusion is violated for a Birkhoff quadrature formula. In this paper an extremal problem with Birkhoff interpolation constraints is discussed, from which a large class of Birkhoff quadrature formulas may be derived. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8998.html} }
TY - JOUR T1 - An Extremal Approach to Birkhoff Quadrature Formulas JO - Journal of Computational Mathematics VL - 5 SP - 459 EP - 466 PY - 2001 DA - 2001/10 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8998.html KW - An extremal approach KW - Birkhoff quadrature formulas AB - As we know, a solution of an extremal problem with Hermite interpolation constraints is a system of nodes of corresponding Gaussian Hermite quadrature formula (the so-called Jacobi approach). But this conclusion is violated for a Birkhoff quadrature formula. In this paper an extremal problem with Birkhoff interpolation constraints is discussed, from which a large class of Birkhoff quadrature formulas may be derived.
Ying Guang Shi. (1970). An Extremal Approach to Birkhoff Quadrature Formulas. Journal of Computational Mathematics. 19 (5). 459-466. doi:
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