Is $m = n^{2}$ here or is it $n^{k}$ for a k-dimensional space?
Edit: Rather, what's meant by a "general mesh" here?
kmcrane
Here $m$ just refers to the number of degrees of freedom, whatever they may be. So for instance, in a triangle mesh it might be the number of vertices. On a 2D grid, it might be the number of grid cells (which is about $m = n^2$ for an $n \times n$ grid).
A "general mesh" means no special structure, i.e., not a regular grid or anything funny like that. A good example would be the triangle meshes we worked with in assignment 2 ("MeshEdit"), which had no particular structure or regularity. Nobody knows how to compute an $O(m \log m)$ spectral transformation for these types of meshes.
Is $m = n^{2}$ here or is it $n^{k}$ for a k-dimensional space?
Edit: Rather, what's meant by a "general mesh" here?
Here $m$ just refers to the number of degrees of freedom, whatever they may be. So for instance, in a triangle mesh it might be the number of vertices. On a 2D grid, it might be the number of grid cells (which is about $m = n^2$ for an $n \times n$ grid).
A "general mesh" means no special structure, i.e., not a regular grid or anything funny like that. A good example would be the triangle meshes we worked with in assignment 2 ("MeshEdit"), which had no particular structure or regularity. Nobody knows how to compute an $O(m \log m)$ spectral transformation for these types of meshes.