A Modified Inverse Iteration Method for Computing the Symmetric Tridiagonal Eigenvectors

MATHEMATICS(2022)

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摘要
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.
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关键词
symmetric tridiagonal matrix,eigenvector solver,clustered eigenpairs,orthogonalization,general Q iteration
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