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The numerical stability of barycentric Lagrange interpolation. (English) Zbl 1067.65016
The author studies the error analysis and the effect of round off error resulting from the interpolation by Lagrange type formulae. He examines the barycentric formula which is defined by $$p_{n}(x)=\left( \sum_{j=0}^{n}\frac{w_{j}}{x-x_{j}}f_{j}\right) /\left( \sum_{j=0}^{n}\frac{w_{j}}{x-x_{j}}\right)$$ and the modified Lagrange formula $$\;$$ $$p_{n}(x)=l(x)\sum_{j=0}^{n}\frac{w_{i}}{x-x_{j}}f_{j}\;\;\;\;$$where $$l(x)=\prod _{j=0}^{n}\left( x-x_{j}\right)$$ and $$w_{j}=1/\prod_{k\neq j}\left( x_{j}-x_{k}\right).$$ Recall that mathematical identities do not necessarily hold in floating point arithmetic. One way to measure the numerical stability of these interpolations is to estimate their condition numbers, out of which the author concludes that the barycentric interpolation should be the method of choice.

##### MSC:
 65D05 Numerical interpolation 41A05 Interpolation in approximation theory
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