The question of setting opts.tol in eigs

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Dan Li
Dan Li 2016-8-8
评论： Sindhuja Parimalarangan 2016-8-12
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 个评论
Sindhuja Parimalarangan
Sindhuja Parimalarangan 2016-8-12
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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