数値微分における補外法の誤差

概要

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We discuss the behavior of round-off error in an extrapolation process in order to obtain an accurate m-th derivative of f(x) under the condition for which f(x) can be computed at any points in the domain. The extrapolation process is applied to a central difference method, however, it is found that the round-off error does not increase so much, even if the number of iterations is quite large. The round-off error does not exceed 25/14 times of the maximum round-off error included in the starting values.
日本応用数理学会の論文
2005-12-25