We compare the Lanczos and MINRES methods for the solution of symmetric linear systems with a linear parameter arising from structural engineering. We show a connection with the Padé-via-Lanczos method. We propose an error estimation for the solution in finite precision arithmetic. The use of reorthogonalization is discussed and practical algorithms are given. The theory is illustrated with numerical examples.
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Karl Meerbergen (2003) studied this question.
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