Partitioning Inverse Monte Carlo Iterative Algorithm for Finding the Three Smallest Eigenpairs of Generalized Eigenvalue Problem

It is well known that the problem of calculating the largest or smallest generalized eigenvalue problem is one of the most important problems in science and engineering 1, 2 . This problem arises naturally in many applications. Mathematically, it is a generalization of the symmetric eigenvalue problem, and it can be reduced to an equivalent symmetric eigenvalue problem. Let A,B ∈ n×n be real symmetric matrices and the matrix B a positive definite matrix. Consider the problem of evaluating the eigenvalues of the pencil A,B , that is, the values for which