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Interpolation is the theory of constructing smooth functions, usually polynomials or trigonometric polynomials, whose graph passes through a number of given points in the plane. Splines and Bézier curves, piecewise linear or cubic interpolation, Lagrange and Hermite interpolation are example topics.

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Given any sequence of interpolating nodes, can we find a continuous function $f$ whose inter...

But it may not be that pessimistic due to the following fact: for any continuous function, there always exists a configuration of interpolation points such that the Lagrangian interpolation converges. …
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