Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix using the Relatively Robust Representations.
The routine computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
T. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
Whenever possible, the routine calls stemr to compute the eigenspectrum using Relatively Robust Representations. stegr computes eigenvalues by the
dqdsalgorithm, while orthogonal eigenvectors are computed from various "good"
representations (also known as Relatively Robust Representations). Gram-Schmidt orthogonalization is avoided as far as possible. More specifically, the various steps of the algorithm are as follows. For the i-th unreduced block of
- Compute, such thatT-σ=iLi*Di*LiTLi*Di*Liis a relatively robust representation.T
- Compute the eigenvalues,λ, ofjLi*Di*Lito high relative accuracy by theTdqdsalgorithm.
- If there is a cluster of close eigenvalues, "choose"σclose to the cluster, and go to Step (a).i
- Given the approximate eigenvalueλofjLi*Di*Li, compute the corresponding eigenvector by forming a rank-revealing twisted factorization.T