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Questions tagged [interpolation-theory]

For questions about interpolation of operators. This includes: real and complex interpolation, interpolation estimates, interpolation spaces. Questions about the estimation of a function from a given input should be asked under the [interpolation] tag instead.

7
votes
2answers
407 views

Analytic “Lagrange” interpolation for a countably infinite set of points?

Suppose I have a finite set of points on the real plane, and I want to find the univariate polynomial interpolating all of them. Lagrange interpolation gives me the least-degree polynomial going ...
3
votes
2answers
353 views

Lagrange linear, quadratic, and cubic interpolations maximum interpolation error functions comparison

Using Theorem 1, calculate that the maximum interpolation error that is bounded for linear, quadratic, and cubic interpolations. Then compare the found error to the bounds given by Theorem 2. The ...
4
votes
2answers
256 views

Who knows this formula for polynomial interpolation?

For my high school math project I studied polynomial interpolation: given a set of points $(x_0,y_0),...,(x_n,y_n)$, find the polynomial of degree $n$ that passes through all points. The solutions by ...