I have a question with some large sparse symmetric matrices of dimensions 100*100. I need to do some computation with the matrices including eigenvalues, eigenvectors, inversion and multiplication by vetors.
I could use BLAS sparse format to store the matrices, but that would be troublesome to calculate the eigenvalues and inversions. However, the matrix has only 5% non-zero values. If I don't use this format, it seems very wasteful.
My question is, whether I should use the packed symmetric form to do all the computations with LAPACK/BLAS Level 2 libraries, or should I use sparse BLAS format to do some simple calculation and convert them to the packed symmetric form to do inversion and factorizations, or use the PARDISO interface?
I'm doing some MCMC algorithm, which needs more than 10,000 iterations, for each iteration, I need to do one matrix inversion, two eigenvalue factorization and several sparse * vector multiplications. So I need some very effective way to perform the program.
Thank you very much.