Solution of Vandermonde systems of equations

Björck, Ȧke; Pereyra, Victor

doi:10.1090/S0025-5718-1970-0290541-1

Solution of Vandermonde systems of equations
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by Ȧke Björck and Victor Pereyra PDF

Math. Comp. 24 (1970), 893-903 Request permission

Abstract:

We obtain in this paper a considerable improvement over a method developed earlier by Ballester and Pereyra for the solution of systems of linear equations with Vandermonde matrices of coefficients. This is achieved by observing that a part of the earlier algorithm is equivalent to Newton’s interpolation method. This allows also to produce a progressive algorithm which is significantly more efficient than previous available methods. Algol-60 programs and numerical results are included. Confluent Vandermonde systems are also briefly discussed.

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Rapid Computation of Interpolation Formulae and Mechanical Quadrature Rules