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Fast algorithms for polynomial interpolation, integration, and differentiation. (English) Zbl 0862.65005
The authors present a group of three algorithms for interpolation, integration and differentiation of functions tabulated at nodes other than Chebyshev.
The interpolation scheme requires $$O(N\log\varepsilon^{-1})$$ arithmetic operations, while for the integration and differentiation schemes are required $$O(N\log N+N\log\varepsilon^{-1})$$ operations, where $$\varepsilon$$ is the precision of computations and $$N$$ is the number of nodes. It should be mentioned that the interpolation and integration schemes are stable, while the differentiation scheme has a condition number proportional to $$N^2$$.
The authors have written FORTRAN implementations of their algorithms using double precision arithmetic. There are included several experiments in order to illustrate the numerical performance of their fast algorithms.

##### MSC:
 65D05 Numerical interpolation 65D32 Numerical quadrature and cubature formulas 65D25 Numerical differentiation 65Y20 Complexity and performance of numerical algorithms
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