I am trying to set up a multigrid solver where I have symmetric matrices M_1,...,M_n and a prolongation matrix P, and I would like to compute N_i=P.transpose() * M_i * P for 1<=i<=n.
1. Is there a faster way to compute N_i then explicitly (pre-)computing the transpose of P and multiplying on both sides?
2. Given that the M_i have identical sparsity structures, can the N_i be computed more efficiently than computing each one independently? (I tried to make a sparse matrix with Scalar types "Array", but that didn't work.)