The question of setting opts.tol in eigs

In the help document of eigs, the opts.tol refers to the Ritz estimate residual. I have two questions:

1. How to calculate the Ritz estimate residual? 2. If using eigs to solve a generalized eigenvalue problem, does matlab use the same criterion RitzRes <= tol*norm(A) or does matlab include the norm of B, such as RitzRes <= tol*(norm(A)+norm(B))?

Thanks

[Sindhuja Parimalarangan]

Hi Dan,

The Ritz estimate residual calculations is based on the algorithms described in the following papers as mentioned at the bottom of the eigs documentation page:

1] Lehoucq, R.B. and D.C. Sorensen, "Deflation Techniques for an Implicitly Re-Started Arnoldi Iteration." SIAM J. Matrix Analysis and Applications. Vol. 17, 1996, pp. 789–821.

[2] Sorensen, D.C., "Implicit Application of Polynomial Filters in a k-Step Arnoldi Method." SIAM J. Matrix Analysis and Applications. Vol. 13, 1992, pp. 357–385.