ON THE CONVERGENCE OF ZERO-FINDING EIGENSOLUTION ALGORITHMS FOR SOLVING NON-LINEAR EIGENVALUE PROBLEMS

This paper presents a convergence theory for non-linear eigenvalue methods. The basic idea of these methods, which have been described by the author in an earlier paper,1 is to apply an eigen-solver in conjunction with a zero- nding technique for solving the non-linear eigenvalue problems. The main focus of the paper is to study the rate of convergence of these techniques when they are applied to solve the dependent symmetric eigenproblems. The results are proved to the zero- nders which are based on rational approximation and they are used to update the eigenvalue .