Question calculate smooth vertice normal without flat normals

My mesh is uniformed structured in the XZ plane like the image shows, with their Y values displaced at random. And I want to calculate each vertex 100% smoothed normal.

What you would to to calculate the smoothed normals for each vertex is to first calculate each normal for each triangle using this or simmilar:

Code (CSharp):

1. triangleNormal = normalize(
2.     cross(
3.         vertice1 - vertice2,
4.         vertice3 - vertice2
5.     )
6. );

And then take the norm of each connected triangle for each vertex, in my case the eight triangles from the neighbouring four quads.

My question is however, very case specific: In that; is there a way for me to calculate the 100% smoothed vertice normals given ONLY the (8+1) vertices around any given vertice in my gridded mesh? Using the fact that they are in a locked grid, and that I know which 9 vertices would change a vertices smooth normal, I should be able to create a really optimized calculation? no?

Im coding it in a compute shader.