Abstract
Often an estimate of a derivative or its range over an interval is desired rather than the derivative itself. Error terms for numerical approximations may sometimes be rigorously estimated in terms of a number of values of the derivative and a “majorant”. We indicate this and propose a technique for the strict estimation of the values of the derivatives in terms of central differences of the function and its “majorant”. We stress strictness and accept less accuracy.
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References
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T. Ström,Comments on Romberg Integration, Rept. NA 69.05 Dept. of Comp. Science, Royal Institute of Technology, Stockholm, Sweden.
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T. Ström,Absolutely Monotonic Majorants—a Tool for Automatic Strict Error Estimation in the Approximate Calculation of Linear Functionals, Rept. NA 70.23 Dept. of Comp. Science, Royal Institute of Technology, Stockholm, Swedene.
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Ström, T. An inclusion formula for derivatives. BIT 11, 196–198 (1971). https://doi.org/10.1007/BF01934368
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DOI: https://doi.org/10.1007/BF01934368