Calculating flux perturbations with a Davidson algorithm

In perturbation calculations, obtaining an accurate flux Shape of a perturb ed core is more difficult than the multiplication factor. Generalized David son algorithms using a symmetric successive overrelaxation preconditioner a re developed to solve the unperturbed eigenvahe problem and the related per turbed eigenvalue problem of large sparse matrices. The bases of the subspa ce obtained from the sequence of solving the unperturbed problem through th e algorithm can be used in the perturbed problem to save computational time . One- and two-dimensional test problems indicate that by incorporating sym metric successive overrelaxation iteration, the optimized relaxation factor and the newly developed shifted form-function vector method for a large pe rturbation a considerable amount of computational time can be saved in the perturbed calculations with accuracy comparable to the existing CITATION co de. This method also provides an efficient means for survey calculations wh ere the requirement of accuracy is not stringent.