How to organize landscape data and how to interpolate?

Question

Mathematics

The idea is to store height data in matrices of N order, while they can be for different levels of detail (by quadTree)
Let's say: 1st level - a matrix covering 100 by 100 meters
2nd level - 50 by 50 meters
3rd level - 25 by 25 meters
so all matrices will have the same number of dots but are designed for different levels of detail. To generate the landscape, it will be necessary to find intermediate values, since the vertices of the geometry themselves will not coincide with the height data.
How good is this idea? What interpolation algorithm will be more plausible to find intermediate heights (in 2 variables)?
I chose this method because it is required to store a large amount of data for an area where high detail is not needed in all places, or rather, high detail is needed only in a small part of the area.