Generalized Hermite formula for the two-sided Lagrange–Sylvester interpolation

The classical Hermite formula of the scalar polynomial interpolation is generalized to the setting of two-sided Lagrange–Sylvester interpolation for matrix polynomials. The formula then is applied to a description of the set of all matrix polynomial solutions to that two-sided interpolation.

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of computational and applied mathematics 2005-01, Vol.173 (2), p.345-358
Hauptverfasser:	Hu, Yong-Jian, Yang, Zheng-Hong, Chen, Gong-Ning
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximations and expansions Exact sciences and technology Hermite formula Lagrange formula Lagrange–Sylvester interpolation Mathematical analysis Mathematics Matrix polynomial McMillan degree Numerical analysis Numerical analysis. Scientific computation Numerical approximation Sciences and techniques of general use Special functions Vandermonde-type matrix
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Beschreibung
Zusammenfassung:	The classical Hermite formula of the scalar polynomial interpolation is generalized to the setting of two-sided Lagrange–Sylvester interpolation for matrix polynomials. The formula then is applied to a description of the set of all matrix polynomial solutions to that two-sided interpolation.
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2004.03.018