Generalized eigenvalue problems: Lanczos algorithm with a recursive partitioning method

In this paper, the computation of the smallest eigenvalues and the corresponding eigenvectors of the generalized eigenvalue problem using Lanczos algorithm with a recursive partitioning method as well as the Sturm sequence-bisection method have been discussed. We have also presented the comparison of the numerical results and the CPU-time between the above two methodologies. Our comparative study indicates that the Lanczos with a recursive partitioning method takes relatively less computing time than that of the Sturm sequence-bisection method.