Contents
What is the problem of interpolation?
Scattered Data Interpolation: Radial Basis and Other Methods The basic problem, referred to as the functional scattered data problem is to find a surface that interpolates or approximates a finite set of points in a k—dimensional space Rk.
What is the drawback of the spline interpolation method?
When the sample points are close together and have extreme differences in value, Spline interpolation doesn’t work as well. This is because Spline uses slope calculations (change over distance) to figure out the shape of the flexible rubber sheet.
Why do we need polynomial interpolation?
Polynomial interpolation is also essential to perform sub-quadratic multiplication and squaring such as Karatsuba multiplication and Toom–Cook multiplication, where an interpolation through points on a polynomial which defines the product yields the product itself.
What are the advantages and disadvantages of Lagrange interpolation?
One advantage (over the Lagrange interpolation method) I know is that, if more interpolation points are added, then there is no need to recompute the previously computed interpolation coefficients. One advantage of the Lagrange interpolation is it is more efficient when interpolating several functions on the same set of points.
What are the disadvantages of using interpolation polynomials?
Those requires still leave the system under-constrained and you need some assumptions (or data) about values beyond the range of data you are fitting, usually an assumption about the 2nd derivative at the two end po
Is it possible to do interpolation in Big extend?
It depends on how you do interpolation in big extend. Unless the function you are trying to approximate is known to look like a polynomial, result will be quite dissatisfactory.
How is the interpolation error related to the distance between data points?
Generally, if we have n data points, there is exactly one polynomial of degree at most n−1 going through all the data points. The interpolation error is proportional to the distance between the data points to the power n. Furthermore, the interpolant is a polynomial and thus infinitely differentiable.