In perturbation calculations, obtaining an accurate flux shape of a perturbed core is more difficult than the multiplication factor. Generalized Davidson algorithms using a symmetric successive overrelaxation preconditioner are developed to solve the unperturbed eigenvalue problem and the related perturbed eigenvalue problem of large sparse matrices. The bases of the subspace obtained from the sequence of solving the unperturbed problem through the algorithm can be used in the perturbed problem to save computational time. One- and two-dimensional test problems indicate that by incorporating symmetric successive overrelaxation iteration, the optimized relaxation factor, and the newly developed shifted form-function vector method for a large perturbation, a considerable amount of computational time can be saved in the perturbed calculations with accuracy comparable to the existing CITATION code. This method also provides an efficient means for survey calculations where the requirement of accuracy is not stringent.