The Rayleigh Quotient Minimization Method For A Class Of Generalized Symmetric Eigenvalue Problems

Based on the paper[9],this paper proposes the Rayleigh quotient minimization method for a class of generalized symmetric eigenvalue problems to solve the minimal eigenpair of generalized symmetric matrices,and the convergence analysis is carried out.The theoretical results show that under certain conditions,the method has global convergence and local cubic convergence.Then we verify the correctness of the theoretical results by numerical experiments.Secondly,this paper discusses the imprecise implementation of the Rayleigh quotient minimization method and its numerical stability,and gives the corresponding numerical experiments,showing the efficiency of the new method for solving the class of generalized symmetric eigenvalue problem.Finally,this paper proposes the Rayleigh quotient minimization block method combined with the subspace iteration method,which is used to solve multiple minimal eigenvalues and corresponding eigenvectors,and the effectiveness of the new method is numerically tested.