# 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.

77 questions
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### What is the geometric meaning of this null-determinant?

While reading about interpolation I came across the following equation in Norlund. It involves determinants and I don't understand it in full yet. I do know how Lagrange and Newton follow by using the ...
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### Is step-wise interpolation possible for a curve which cannot be represented by a function?

According to definition of Interpolation - A function $y=P(x)$ can interpolate a set of data points if $y_i = P(x_i) | 1\le i\le n$ for the set of data points being - $(x_1,y_1), ..... , (x_n,y_n)$. ...
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### Use 1-degree Chebyshev polynom to approximate $\cos(x)$ and calculate the error

The task is to give for $\cos(x)$ the nodes of the interpolation polynom of degree 1 that approximates the function on $[-\pi,\pi]$ the best as well as the related error. I want to solve this task ...
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### What is the Lagrange Interpolation polynomial of $1/{(x-1)}$?

So what is the value of $$L[x_0,x_1,\ldots,x_n; \; 1/{(x-1)}]=\text{?}$$ I tried writing a Mathematica program to compute it, but I couldn't figure it out...
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### Can I decompose the Lagrange interpolating polynomial of the sum of 2 functions into 2 separate Lagrange polynomials? [closed]

For example:L[x0,x1,...,xn;f+g]=?=L[x0,x1,...,xn;f] + L[x0,x1,...,xn;g] where f and g are ordinary functions, not neccessarily polynomials......