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Non-Unit Bidiagonal Matrices for Factorization of Vandermonde Matrices

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Abstract:

A non-unit bidiagonal matrix and its inverse with simple structures are introduced. These matrices can be constructed easily using the entries of a given non-zero vector without any computations among the entries. The matrix transforms the given vector to a column of the identity matrix. The given vector can be computed back without any round off error using the inverse matrix. Since a Vandermonde matrix can also be constructed using given n quantities, it is established in this paper that Vandermonde matrices can be factorized in a simple way by applying these bidiagonal matrices. Also it is demonstrated that factors of Vandermonde and inverse Vandermonde matrices can be conveniently presented using the matrices introduced here.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 12)
Pages:
1-13
DOI:
10.18052/www.scipress.com/BMSA.12.1
Citation:
R. Purushothaman Nair "Non-Unit Bidiagonal Matrices for Factorization of Vandermonde Matrices", Bulletin of Mathematical Sciences and Applications, Vol. 12, pp. 1-13, 2015
Online since:
May 2015
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