I have seen efficient implementations of LU decomposition for tridiagonal and penta diagonal matrices. I have a banded diagonal matrix that is huge 100k rows by 100k columns, but each row has only 27 elements. The matrix looks like a tridiagonal matrix of tridiagonal, tridiagonal matrices.
To make myself clear, imagine the matrix as a tridiagonal matrix, where each one of the 3 "diagonals" is a tridiagonal itself, and each of them is a tridiagonal (hence the 27 elements per row: 333). Is there an efficient parallel algorithm to factorize this matrix? Can I apply divide and conquer on it?
The matrix is sparse (CSR format) if this is going to help.
I am an absolute beginner, but I am trying to learn computational techniques for linear algebra, so please go easy on me.
If the fact that it is a diagonal matrix is not going to help, is there another parallel algorithm to factorize a sparse matrix efficiently? Can someone guide me please?