Hello,

I need to estimate error bounds for the eigenvalues and eigenvectors of a self-adjoint matrix of the double complex type. For their LAPACK counterparts, I found a simple recipe at: http://www.netlib.org/lapack/lug/node89.html . On this page, there is a FORTRAN code fragment that calculates the approximate error bounds. I would like to know whether the same code would produce reasonable estimates of error bounds for the eigenvalues and eigenvectors returned by SelfAdjointEigenSolver or not. I suppose this would be the case if the algorithms used in Eigen and ZHEEV were the same. If not, I hope the same procedure nevertheless applies since the formulas look pretty generic. For instance, the error bound on the eigenvalues is simply the machine epsilon times the largest absolute eigenvalue. I need to catch in particular a potential accuracy loss due to a large hierarchy among the eigenvalues. I would also appreciate advice on error bounds for SVD of a complex square matrix. The LAPACK recipe for this is at: http://www.netlib.org/lapack/lug/node96.html .

Best,
Jae-hyeon

yes, these discussions of the Lapack user guide also apply to Eigen's algorithm.

Many thanks for the clear reply!