### Eigenvectors from Eigenvalues

Posted:

**Thu Nov 14, 2019 1:37 pm**I'm sure the following publication has not gone entirely unnoticed in the LAPACK community:

Eigenvectors from Eigenvalues

https://arxiv.org/abs/1908.03795

This is a pretty astoundingly elegant result. If there is a way to compute the required submatrix eigenvalues of symmetric tridiagonal matrices efficiently, maybe even sharing computations between them, we could calculate eigenvectors directly from these eigenvalues. This could conceivably improve both the accuracy and speed of obtaining all eigenvectors. Does anybody already know whether this is possible?

Eigenvectors from Eigenvalues

https://arxiv.org/abs/1908.03795

This is a pretty astoundingly elegant result. If there is a way to compute the required submatrix eigenvalues of symmetric tridiagonal matrices efficiently, maybe even sharing computations between them, we could calculate eigenvectors directly from these eigenvalues. This could conceivably improve both the accuracy and speed of obtaining all eigenvectors. Does anybody already know whether this is possible?