Abstract
In this paper a new algorithm for solving special Vandermonde systems is presented, useful when then points defining the matrix are thek th roots ofm complex numbers (n=km); if they are real and positive andn=2m, the usual case of real points symmetrically ranged around zero is obtained. The algorithm is based on an inverse matrix formulation by means of the Kronecker product and is particularly suitable for parallel implementation. Its computational complexity is analysed and compared both in the sequential and parallel formulation.
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References
S. Barnett, Matrix differential equations and Kronecker products, SIAM J. Appl. Math. 24 (1973) 1–5.
A. Björck and V. Pereyra, Solution of Vandermonde systems of equations, Math. Comp. 24 (1970) 893–904.
J.G. Clunie and J.C. Mason, Norms of analytic interpolation projections on general domains, J. Approx. Theory 41 (1984) 149–158.
N.J. Higham, Error analysis of the Björck-Pereyra algorithm for solving Vandermonde systems, Num. Math. 50 (1987) 613–632.
G.H. Golub and C.F. van Loan,Matrix Computations, 2nd ed. (The Johns Hopkins University Press, 1989).
J. Szabados and R.S. Varga, On the convergence of complex interpolating polynomials, J. Approx. Theory 36 (1982) 346–363.
W.P. Tang and G.H. Golub, The block decomposition of a Vandermonde matrix and its applications, BIT 21 (1981) 505–517.
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Communicated by C. Brezinski
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Tommasini, T. A new algorithm for special Vandermonde systems. Numer Algor 2, 299–306 (1992). https://doi.org/10.1007/BF02139470
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DOI: https://doi.org/10.1007/BF02139470