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Solution of Vandermonde systems of equations

Math. Comp.
Pub Date  : 1970-01-01
DOI : 10.1090/s0025-5718-1970-0290541-1

{Ake Bj{örck , Victor Pereyra

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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中文翻译
范德蒙方程组的解
我们在本文中获得了对早先由 Ballester 和 Pereyra 开发的用于求解具有 Vandermonde 系数矩阵的线性方程组的方法的显着改进。这是通过观察早期算法的一部分等效于牛顿插值方法来实现的。这也允许产生比以前可用的方法明显更有效的渐进算法。包括 Algol-60 程序和数值结果。还简要讨论了 Confluent Vandermonde 系统。
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