Computation of a few smallest eigenvalues and their eigenvectors for large sparse SPD matrices

The algorithm and the code for computing several eigenvalues and their corresponding eigenvectors of a large sparse symmetric positive definite (SPD) matrix, which arises as a result of grid approximations (FDM, FEM, or FVM) of multidimensional boundary value problems (BVPs) are described. The preconditioned inverse iteration (PINVIT) method is implemented by using the explicit incomplete factorization method with conjugate gradient acceleration for solving an auxiliary linear system of equations. The numerical results are presented and discussed.