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In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem ...

Let $A$ be a matrix of order $n$ and let $\clu\subset\comp^{n}$ be a subspace of dimension $k$. In this note we determine a matrix $E$ of minimal norm such that $\clu$ is a Krylov subspace of $A+E$. (Cross-referenced ...