# Questions tagged [interpolation]

Interpolation is the process of estimating the values of a function, when the function's values are known only at a particular set of points. Questions on interpolation in one or more dimensions, as well as algorithms for doing so, should have this tag.

175 questions
Filter by
Sorted by
Tagged with
25k views

### What is the preferred and efficient approach for interpolating multidimensional data?

What is the preferred and efficient approach for interpolating multidimensional data? Things I'm worried about: performance and memory for construction, single/batch evaluation handling dimensions ...
2k views

### Why do equi-spaced points behave badly?

Experiment description: In Lagrange interpolation, the exact equation is sampled at $N$ points (polynomial order $N - 1$) and it is interpolated at 101 points. Here $N$ is varied from 2 to 64. Each ...
5k views

### What is the best way to find discontinuities of a black-box function?

It was suggested that this might be a better place for this question than Mathematics Stack Exchange where I asked it before. Suppose one has a black-box function which can be evaluated anywhere (...
2k views

### Example of a continuous function that is difficult to approximate with polynomials

For teaching purposes I'd need a continuous function of a single variable that is "difficult" to approximate with polynomials, i.e. one would need very high powers in a power series to "fit" this ...
6k views

### Efficient interpolation method for unstructured grids?

I would like to know a good method for interpolating data between two unstructured grids, where one grid is a coarser version of the other. Efficiency is very important to me since I'm solving a ...
2k views

### How to interpolate multipoint data to the cell centres of an unstructured mesh?

I have sets of multipoint field data, each point data set relates to a single cell of an unstructured mesh. The goal is to interpolate the data to the cell centre, directly or indirectly, in the most ...
198 views

### Implications of thermodynamic inconsistency in CFD calculations

During my PhD work, I had to use tabulated values of thermodynamic properties of gases in some Computational Fluid Dynamics (CFD in short) simulations. My tables are discretized in temperature and ...
3k views

### Do RBF kernel matrices tend to be ill-conditioned?

I use RBF kernel function to implement one kernel based machine learning algorithm(KLPP), the resulting kernel matrix $K$ $$K(i,j)= \exp\left({\frac{-(x_{i}-x_{j})^2}{ \sigma_{m}^2}}\right)$$ is ...
2k views

### When we use Bernstein polynomials in application

When it is preferable to use Bernstein polynomials to approximate a continuous function instead of using the only following preliminary Numerical Analysis methods: "Lagrange Polynomials", "Simple ...