Iterative method for a class of nonlinear eigenvalue problems

Abstract

Let H Be a complex and separable Hilbert space and consider in H the nonlinear eigenvalue problem where A, B, and C belong to the class of unbounded nonsymmetric operators, which are K- positive K-symmetric. Sufficient conditions insuring the existence of the eigenvalues of (i) are investigated. An iterative method for approximating the eigenvalues of (i) is developed and its convergence proved. Some numerical examples are given to illustrate the theory.

Keywords:

• Nonlinear eigenvalue problem.
• symmetrizable operators
• K-positive
• K-symmetric
• iterative method