A Study On The Accelerated-strategies Of Subspace Iteration Methods

Subspace iteration method is one of efficient numerical methods for solution of large sparse symmetric eigenproblems. The efficient of subspace iteration method is dependent on the selection of initial vectors and convergence rate. Many accelerated subspace iteration methods is based on these two aspects. For obtain a higher convergence rate, the paper presents following accelerated-strategies based on summary of the existing accelerated methods.Firstly, for selecting the best number of iterative vectors which cause the total operation to be smallest, the paper analysis the parameters influence the total operation of algorithm. According to these parameters, a new method is proposed. Secondly, in order to select best initial vectors, a new selection method is proposed based on the circle theorem.Then, using the accelerated-strategy of extra inverse iteration which is presented by Qian and Lam, the improvement method is proposed. Lam and Bertolini select vectors that need to be extra inverse iteration by convergence rate. For reduction the error of this method, the new method using consistent eigenvalues is proposed. And one new method for determination biggest iteration step is introduced. Two algorithms are presented for different problems.Finally, using the accelerated-strategy of over-relaxation method, a method which improves the difficulty of computing over-relaxation factors is proposed. And the numerical examples of different algorithms are presented at the end of every chapter.