A sparse matrix representation will dramatically reduce the computational complexity

• With a dense matrix, the algorithm leads to \( \Oof{N_x^3} \) operations
• Utilizing the sparsity, the algorithm has complexity \( \Oof{N_x} \)!
• scipy.sparse enables storage and calculations with the three nonzero diagonals only

# Representation of sparse matrix and right-hand side
diagonal  = zeros(Nx+1)
lower     = zeros(Nx)
upper     = zeros(Nx)
b         = zeros(Nx+1)