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The authors analyse some aspects of the numerically well-behaved Lanczos method of tri-diagonalising a matrix and the mathematically equivalent but numerically disastrous method of moments. It is shown how the elements of the Lanczos tri-diagonal matrix depend only on certain identifiable contributions to the moments, these contributions being those that do not duplicate any information about the matrix already contained in lower moments, all other contributions cancelling exactly.
Whitehead et al. (Thu,) studied this question.