Lecture notes in numerical linear algebra Arnoldi method convergence 1 Convergence of the Arnoldi method for eigenvalue problems
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چکیده
It is very natural to associate the accuracy of the eigenvector with this quantity from a geometric perspective. The indicator in the right-hand side of (1.1) is called (the norm of) the orthogonal complement of the projection of xi onto the space spanned by Q and it can be interpreted as the sine of the canonical angle between the Krylov subspace and an eigenvector. For the moment, we will only justify this indicator with this geometric reasoning and the following observation:
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