Postprocessing and Accuracy Checking

   

The eigenvalues and eigenvectors of ${\bf A}$ and can be extracted with a call to dneupd when using drivers dndrv1 - dndrv4. However, since the eigenvalues computed for OP by the drivers dndrv5 and dndrv6 are related to the eigenvalues of ${\bf A}{\bf x}={\bf M}{\bf x}\lambda$by

respectively. These equations do not have a unique solution and it appears to be difficult to match the correct solution with a given eigenvector. Thus, the Rayleigh Quotient must be formed by the user to obtain the eigenvalue corresponding to the eigenvector This will be done automatically in dneupd in a later release of ARPACK.

Once the converged eigenvalues and eigenvectors have been obtained the user may check the accuracy of the results by computing the direct residuals and for a standard or generalized eigenvalue problems. Residual checking is provided in all drivers.