论文信息 - A comparison of the average case numerical condition of the power and bernstein polynomial bases

A comparison of the average case numerical condition of the power and bernstein polynomial bases

The relative numerical condition of a root x 0, of arbitrary multiplicity, of a polynomial p(x) in the power and Bernstein bases is considered. The polynomial equation p(x)=0 and the linear algebraic equation that defines the transformation between the bases are used to show that the relative numerical condition of x 0 in the bases is strongly dependent on the numerical condition of this equation. Furthermore, as the multiplicity of x o increases for a given polynomial order, the relative numerical condition of x 0 approaches unity. Computational examples that illustrate the theoretical results are presented.

Joab R. Winkler

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