On the inversion of the Vandermonde matrix

@article{Eisinberg2006OnTI,
  title={On the inversion of the Vandermonde matrix},
  author={A. Eisinberg and G. Fedele},
  journal={Appl. Math. Comput.},
  year={2006},
  volume={174},
  pages={1384-1397}
}
  • A. Eisinberg, G. Fedele
  • Published 2006
  • Mathematics, Computer Science
  • Appl. Math. Comput.
  • Abstract The inversion of the Vandermonde matrix has received much attention for its role in the solution of some problems of numerical analysis and control theory. This work deals with the problem of getting an explicit formula for the generic element of the inverse. We derive two algorithms in O(n2) and O(n3) and compare them with the Parker–Traub and the Bjorck–Pereyra algorithms. 
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    References

    SHOWING 1-10 OF 28 REFERENCES
    On the Inversion of Vandermonde Matrix
    • 6
    The inversion of the Vandermonde matrix and transformation to the Jordan canonical form
    • 53
    The Fast Generalized Parker-Traub Algorithm for Inversion of Vandermonde and Related Matrices
    • 52
    • Highly Influential
    • PDF
    Lower bounds for the condition number of Vandermonde matrices
    • 136
    Vandermonde matrices on Chebyshev points
    • 7
    Vandermonde systems on equidistant nodes in [0, 1]: accurate computation
    • 6
    • PDF
    Vandermonde matrices on integer nodes
    • 14
    Solution of Vandermonde Systems of Equations
    • 356
    • PDF
    Vandermonde systems on Gauss-Lobatto Chebyshev nodes
    • 10
    • PDF