Non-Unit Bidiagonal Matrices for Factorization of Vandermonde Matrices
2015 ◽
Vol 12
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pp. 1-13
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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.
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2010 ◽
Vol 42
(1)
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pp. 210-225
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