Subspace Iteration Method For Solving Eigenvalues Of Large Sparse Matrix

This dissertation studies the subspace iteration method for solving large sparsestandard eigenvalue problems and gyroscopic eigenvalue problems and emphasizeson studying the complex subspace iteration method for solving gyroscopic eigenvalueproblems. Firstly, we propose the accelerated preconditioning subspace iteration by usingChebyshev polynomials. The main part of this hybrid algorithm is a Chebysheviteration which applies Chebyshev polynomials to act on initial vectors and makes theobtained vectors close to the wanted eigenvalues. Secondly, we propose the complexsubspace iteration method for solving damped gyroscopic eigenvalue problems andanalyze its convergence. It's the generalized form of the complex subspace iterationmethod for solving eigenvalue problems of nonclassically damped structures. In orderto improve the complex subspace iteration method for solving undamped gyroscopiceigenvalue problems, we apply the special properties of undamped gyroscopiceigenvalues to it, so we propose double inverse iteration method and double subspaceiteration method. Theoretical analyse and numerical results show that the acceleratedpreconditioning subspace iteration by using Chebyshev polynomials is superior to thepreconditioning subspace iteration, the complex subspace iteration method for solvingdamped gyroscopic eigenvalue problems is better than the dynamic orthogonalityreduction method and double inverse iteration method and double subspace iterationmethod are the improving of the complex subspace iteration method for solvingundamped gyroscopic eigenvalue problems.