The question of setting opts.tol in eigs

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Dan Li
Dan Li on 8 Aug 2016
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
  1 Comment
Sindhuja Parimalarangan
Sindhuja Parimalarangan on 12 Aug 2016
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.

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