Numerical comparison of iterative eigensolvers for large sparse symmetric positive definite matrices Original Research Article

The Jacobi–Davidson (JD) method has been recently proposed for the evaluation of the partial eigenspectrum of large sparse matrices. In this work we report a set of numerical experiments that compare this method with other previously proposed techniques; deflation accelerated conjugate gradient (DACG) and Lanczos (ARPACK), on large sparse symmetric matrices. The results obtained by JD and DACG are benchmarked against those obtained with ARPACK in terms of computational time for the evaluation of s (s⩽100) leftmost eigenpairs. The comparison is performed on a number of matrices, with dimensions up to a few hundred thousands, arising from the discretization of the diffusion equation by means of finite element, mixed finite element, and finite difference techniques. The results show that DACG and JD are equally more efficient than ARPACK for a small number of eigenpairs, with DACG more performing for small s and particularly for s=1, while ARPACK tends to become competitive when 40 or more eigenpairs are sought. For the largest and worst conditioned matrix DACG proves the only viable alternative.