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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.  

  • Keywords

An extremal approach, Birkhoff quadrature formulas.

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COPYRIGHT: © Global Science Press

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@Article{JCM-19-459, author = {Shi , Ying-Guang}, 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 AU - Shi , Ying-Guang 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, 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.  

Shi , Ying-Guang. (2001). An Extremal Approach to Birkhoff Quadrature Formulas. Journal of Computational Mathematics. 19 (5). 459-466. doi:
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