A Modified Inverse Iteration Method for Computing the Symmetric Tridiagonal Eigenvectors - Wei Chu; Yao Zhao; Hua Yuan (Mathematics, 2022)
This paper presents a novel method for computing the symmetric tridiagonal eigenvectors, which is the modification of the widely used Inverse Iteration method. We construct the corresponding algorithm by a new one-step iteration method, a new reorthogonalization method with the general Q iteration and a significant modification when calculating severely clustered eigenvectors. The numerical results show that this method is competitive with other existing methods, especially when computing part eigenvectors or severely clustered ones.