Displacement structure approach to Cauchy and Cauchy–Vandermonde matrices: inversion formulas and fast algorithms

The confluent Cauchy and Cauchy–Vandermonde matrices are considered, which were studied earlier by various authors in different ways. In this paper, we use another way called displacement structure approach to deal with matrices of this kind. We show that the Cauchy and Cauchy–Vandermonde matrices s...

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Vydáno v:Journal of computational and applied mathematics Ročník 138; číslo 2; s. 259 - 272
Hlavní autoři: Yang, Zheng-Hong, Hu, Yong-Jian
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 15.01.2002
Elsevier
Témata:
Algebra
Cauchy–Vandermonde matrix
Displacement structure
Exact sciences and technology
Fast algorithm
Hermite rational interpolation
Inversion formula
Linear and multilinear algebra, matrix theory
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Inversion formula
Cauchy–Vandermonde matrix
Hermite rational interpolation
15A57
65D05
Fast algorithm
Displacement structure
Cauchy matrix
Confluent matrix
Linear algebra
Matrix calculus
Algorithm
Matrix equation
Cauchy Vandremonde matrix
Vandermonde matrix
ISSN:0377-0427, 1879-1778
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Shrnutí:The confluent Cauchy and Cauchy–Vandermonde matrices are considered, which were studied earlier by various authors in different ways. In this paper, we use another way called displacement structure approach to deal with matrices of this kind. We show that the Cauchy and Cauchy–Vandermonde matrices satisfy some special type of matrix equations. This leads quite naturally to the inversion formulas and fast algorithms for matrices of this kind.
Bibliografie:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(01)00378-8