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A convergence analysis for the nonsymmetric Lanczos algorithm is presented. By using a tridiagonal structure of the algorithm, some identities concerning Ritz values and Ritz vectors are established and used to derive approximation bounds. In particular, the analysis implies the classical results for the symmetric Lanczos algorithm.doi:10.2307/2008401 fatcat:u6mxnqvr4jem7fbksar3vaerze