The Quadratic Approximation Methods For Solving Nonlinear Eigenvalue Problems

The numerical methods for solving nonlinear eigenvalue problems are considered in this thesis.Based on the second-order approximation of matrix-valued functions, the nonlinear eigenvalueproblems are transformed into the quadratic eigenvalue problems. A successive quadraticapproximation method for solving the nonlinear eigenvalue problems is presented, and theconvergence analysis of the method is given. Combining with the modified SOAR method,Jacobi-Davidson method and refined second residual iteration method for solving the quadraticeigenvalue problems, some quadratic approximation methods for solving the nonlinear eigenvalueproblems are developed. Numerical results show that the proposed methods are efficient.