Explicit factorization of the Vandermonde matrix
نویسندگان
چکیده
منابع مشابه
Vandermonde Factorization of a Hankel Matrix ?
We show that an arbitrary Hankel matrix of a nite rank admits a Vandermonde decomposition: H = V T DV , where V is a con-uent Vandermonde matrix and D is a block diagonal matrix. This result was rst derived by Vandevoorde; our contribution here is a presentation that uses only linear algebra, speciically, the Jordan canonical form. We discuss the choices for computing this decomposition in only...
متن کاملOn the LU factorization of the Vandermonde matrix
In this paper, the author gives a simpler alternative approach to the LU factorization and 1-banded factorization of the Vandermondematrix, and obtains explicit formulas of the triangular factors and 1-bandedmatrices by using symmetric functions. © 2004 Elsevier B.V. All rights reserved.
متن کاملLU factorization of the Vandermonde matrix and its applications
A scaled version of the lower and the upper triangular factors of the inverse of the Vandermonde matrix is given. Two applications of the q-Pascal matrix resulting from the factorization of the Vandermonde matrix at the q-integer nodes are introduced. c © 2007 Elsevier Ltd. All rights reserved.
متن کاملA General Vandermonde Factorization of a Hankel Matrix ?
It is shown that an innnite Hankel matrix of a nite rank (or a nite Hankel matrix) admits a generalized Vandermonde decomposition H = V T DV , where V is a generalized Vandermonde matrix, and D is a block diagonal matrix. The full structure of this decomposition was rst fully discussed by Vandevoorde 9], but the development here is based solely on linear algebra considerations, speciically the ...
متن کاملOn a Special Generalized Vandermonde Matrix and Its Lu Factorization
We consider a special class of the generalized Vandermonde matrices and obtain an LU factorization for its member by giving closed-form formulae of the entries of L and U . Moreover, we express the matrices L and U as products of 1-banded (bidiagonal) matrices. Our result is applied to give the closed-form formula of the inverse of the considered matrix.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2000
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(00)00124-5