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On a number of issues generalized Vandermonde matrix

Author: QiaoYun
Tutor: WuHuaZuo
School: Anhui University
Course: Applied Mathematics
Keywords: Vandermonde matrix Generalized Vandermonde matrix Hankel matrix Toeplitz matrices Interpolation
CLC: O151.21
Type: Master's thesis
Year: 2007
Downloads: 155
Quote: 0
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Abstract


This paper focuses on Vandermonde matrices and several generalized Vandermonde matrix ( such as the Cauchy-Vandermonde matrix , confluent Vandermonde matrix form confluent Vandermonde matrix functions and q-adic Vandermonde matrix ) discussions summarized several of their properties . First introduced the concept of Vandermonde matrices and some properties, such as polynomial interpolation problem with the link between the triangle and the Vandermonde matrix decomposition . Secondly, this paper several generalized Vandermonde matrix are summarized and derivation . For example , Cauchy-Vandermonde matrix type in the Lagrange interpolation problem can be seen as its coefficient matrix . Meanwhile this paper Cauchy-Vandermonde matrices other properties , such as the inverse matrix representation and so on. In addition , around the confluence Vandermonde matrix , on the one hand , given its significance interpolation to obtain confluent Vandermonde matrix and the link between Hermite interpolation problem : on the other hand gives the other determinant of recurrence formula . For the functional form of the confluence of the Vandermonde matrix and the q-adic Vandermonde matrix , also got their contact with the relevant interpolation problem as well as other properties . Finally, given the degree of a node having the same weight sequence of points , corresponding to the confluence Vandermonde matrix structure and a special Hankel matrix , given the relationship between the two matrices . In addition , the corresponding nodes construct a special kind of Toeplitz matrix , similar to a series of related properties can be obtained .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Theory of algebraic equations,linear algebra > Linear Algebra > Matrix theory
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