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Volume 21, Issue 2
On the Generalized Inverse Neville-Type Matrix-Valued Rational Interpolants

Zhibing Chen

J. Comp. Math., 21 (2003), pp. 157-166.

Published online: 2003-04

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  • Abstract

 A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson inverse for matrices, with scalar numerator and matrix-valued denominator. In this respect, it is essentially different from that of the previous works [7, 9], where the matrix-valued rational interpolants is in Thiele-type continued fraction form with matrix-valued numerator and scalar denominator. For both univariate and bivariate cases, sufficient conditions for existence, characterisation and uniqueness in some sense are proved respectively, and an error formula for the univariate interpolating function is also given. The results obtained in this paper are illustrated with some numerical examples.

  • Keywords

Generalized inverse for matrices, Neville-type, Rational interpolants.

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COPYRIGHT: © Global Science Press

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@Article{JCM-21-157, author = {Zhibing Chen}, title = {On the Generalized Inverse Neville-Type Matrix-Valued Rational Interpolants}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {2}, pages = {157--166}, abstract = {

 A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson inverse for matrices, with scalar numerator and matrix-valued denominator. In this respect, it is essentially different from that of the previous works [7, 9], where the matrix-valued rational interpolants is in Thiele-type continued fraction form with matrix-valued numerator and scalar denominator. For both univariate and bivariate cases, sufficient conditions for existence, characterisation and uniqueness in some sense are proved respectively, and an error formula for the univariate interpolating function is also given. The results obtained in this paper are illustrated with some numerical examples.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10268.html} }
TY - JOUR T1 - On the Generalized Inverse Neville-Type Matrix-Valued Rational Interpolants AU - Zhibing Chen JO - Journal of Computational Mathematics VL - 2 SP - 157 EP - 166 PY - 2003 DA - 2003/04 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10268.html KW - Generalized inverse for matrices, Neville-type, Rational interpolants. AB -

 A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson inverse for matrices, with scalar numerator and matrix-valued denominator. In this respect, it is essentially different from that of the previous works [7, 9], where the matrix-valued rational interpolants is in Thiele-type continued fraction form with matrix-valued numerator and scalar denominator. For both univariate and bivariate cases, sufficient conditions for existence, characterisation and uniqueness in some sense are proved respectively, and an error formula for the univariate interpolating function is also given. The results obtained in this paper are illustrated with some numerical examples.

Zhibing Chen. (2003). On the Generalized Inverse Neville-Type Matrix-Valued Rational Interpolants. Journal of Computational Mathematics. 21 (2). 157-166. doi:
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