Geodesic
First-order perturbation theory for the symmetric lanczos algorithm
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 3, pp. 391-399

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Sensitivity with respect to infinitesimal perturbations of a matrix is analyzed for orthonormal bases in Krylov subspaces constructed by using the symmetric Lanczos iteration. Exact expressions for the corresponding condition numbers are derived, which makes it possible to efficiently calculate these numbers. 
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     author = {A. N. Malyshev and M. Sadkane},
     title = {First-order perturbation theory for the symmetric lanczos algorithm},
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     number = {3},
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A. N. Malyshev; M. Sadkane. First-order perturbation theory for the symmetric lanczos algorithm. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 3, pp. 391-399. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_3_a3/