Non-Unit Bidiagonal Matrices for Factorization of Vandermonde Matrices

R. Purushothaman Nair
2015 Bulletin of Mathematical Sciences and Applications  
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
more » ... rmonde 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.
doi:10.18052/www.scipress.com/bmsa.12.1 fatcat:6epx2moa5fagzjfzghczmeylzm