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2-Norm Error Bounds and Estimates for Lanczos Approximations to Linear Systems and Rational Matrix Functions
The Lanczos process constructs a sequence of orthonormal vectors $v_m$ spanning a nested sequence of Krylov subspaces generated by a hermitian matrix $A$ and some starting vector $b$. In this paper we show how to cheaply recover a secondary Lanczos process starting at an arbitrary Lanczos vector $v_m$. This secondary …