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Vandermonde matrix
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(Definition)
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A Vandermonde matrix is any
 matrix of the form
Vandermonde matrices usually arise when considering systems of polynomials evaluated at specific points (i.e. in interpolation or approximation). This may happen, for example, when trying to solve for constants from initial conditions in systems of differential equations or recurrence relations.
Vandermonde matrices also appear in the computation of FFTs (Fast Fourier Transforms). Here the fact that Vandermonde systems  can be solved in
 flops by taking advantage of their recursive block structure comes into play.
- Golub and Van Loan, Matrix Computations, Johns Hopkins University Press 1993
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"Vandermonde matrix" is owned by akrowne.
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(view preamble)
Cross-references: Transforms, recurrence relations, differential equations, initial conditions, approximation, interpolation, points, polynomials, matrix
There are 5 references to this entry.
This is version 1 of Vandermonde matrix, born on 2002-09-28.
Object id is 3481, canonical name is VandermondeMatrix.
Accessed 10095 times total.
Classification:
| AMS MSC: | 65T50 (Numerical analysis :: Numerical methods in Fourier analysis :: Discrete and fast Fourier transforms) | | | 65F99 (Numerical analysis :: Numerical linear algebra :: Miscellaneous) | | | 15A57 (Linear and multilinear algebra; matrix theory :: Other types of matrices ) |
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Pending Errata and Addenda
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