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Generalized-confluent Cauchy and Cauchy–Vandermonde matrices

✍ Scribed by Zheng-Hong Yang; Gong-Ning Chen

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
235 KB
Volume
308
Category
Article
ISSN
0024-3795

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✦ Synopsis

The so-called Generalized-Confluent Cauchy-Vandermonde (GCCV) matrices of the form [C,V] consisting of a generalized-confluent Cauchy part C and a generalized-confluent Vandermonde part V are considered. A simple relationship between GCCV and classical confluent Cauchy-Vandermonde (CCV) matrices is given. This leads to the reduction of the displacement structure, inversion formulas and factorizations of GCCV matrices, and the interpolation interpretations of linear systems with such GCCV coefficient matrices as tangential interpolation problems to the corresponding results of CCV matrices. The criteria of invertibility and (left, right) inversion formulas for such matrices are given. All results are stated for the general case of multiple interpolation nodes, extending the work of Heinig, and Vavȓín among others.

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