Final answer:
The student needs to derive and plot interpolation functions for a 1D problem using different methods like Cubic Spline, Barycentric Lagrange, Hermite, and Linear Interpolation and evaluate these interpolations at specific points in Excel or MATLAB.
Thebright answer is d) Linear Interpolation
Step-by-step explanation:
The student is asking to derive and plot interpolation functions for a 1D problem using different interpolation techniques such as Cubic Spline, Barycentric Lagrange, Hermite, and Linear Interpolation.
To do this, one needs to understand the basics of each interpolation method and apply them to the given problem, often involving calculating coefficients and evaluating functions at specific points.
For a Cubic Spline, it involves finding a cubic polynomial between each pair of points. Barycentric Lagrange is a form of Lagrange interpolation that uses weights to improve numerical stability.
Hermite interpolation uses not only the values but also the derivatives of the function. Linear Interpolation is the simplest, using straight lines between points.
Plotting these functions in Excel or MATLAB requires setting up the interpolation functions and evaluating them across the desired range of x.
Each interpolation will yield a different shape of the curve depending on the method used, reflecting how they handle the trade-off between accuracy and smoothness.
Thebright answer is d) Linear Interpolation