Abstract
A practical approach is proposed to the problem of simultaneously computing a function, its partial derivatives with respect to all the variables, and an estimate of the rounding error incurred in the computed value of the function. Theoretically, it has a complexity at most a constant times as large as that of evaluating the function alone, the constant being independent of the number of variables of the function, and it is an alternative graphical interpretation of W. Baur and V. Strassen’s results, with some generalizations. Practically, it is stated in a form easily implementable as a computer program, which enables us to automatically compute the derivatives if we are given only the program for computing the function. Remarks are added also on the cases of several functions, of higher derivatives and of non-straght-line programs, and on application to problems containing differential equations.
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Iri, M. Simultaneous computation of functions, partial derivatives and estimates of rounding errors —Complexity and practicality—. Japan J. Appl. Math. 1, 223–252 (1984). https://doi.org/10.1007/BF03167059
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DOI: https://doi.org/10.1007/BF03167059