### Computing a Subinterval of the ImageComputing a Subinterval of the Image

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 Author Richman, Paul L. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1974 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract The problem of computing a desired function value to within a prescribed tolerance can be formulated in the following two distinct ways: $\textit{Formulation}$ I: Given x and ∈ > 0, compute $\textit{f}(x)$ to within ∈. $\textit{Formulation}$ II: Given only that x is in a closed interval X, compute a subinterval of the image, $\textit{f}(X)$ = ${\textit{f}(x)$ : x ∈ X}. The first formulation is applicable when x is known to arbitrary accuracy. The second formulation is applicable when x is known only to a limited accuracy, in which case the tolerance is prescribed albeit indirectly by the interval X, and one must be satisfied with all or part of the set $\textit{f}(X)$ of possible function values.Elsewhere the author has presented an efficient solution to Formulation I for any rational $\textit{f}$ and many nonrational $\textit{f}.$ B. A. Chartres has presented an efficient solution to Formulation II for a very restricted class of rational $\textit{f}$ and for a few nonrational $\textit{f}.In$ this paper a solution to Formulation II for the arbitrary nonconstant rational $\textit{f}$ is presented. By bounding $\textit{df/dx}$ away from zero over some subset of X, it is shown how to reduce Formulation II to Formulation I, yielding the solution given here.In generalizing to vector-valued functions f, Chartres has solved Formulation II only for rational f which satisfy a linear system of equations, while this paper presents a solution for arbitrary non-degenerate rational vector-valued f. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1974-07-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 21 Issue Number 3 Page Count 5 Starting Page 454 Ending Page 458

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Source: ACM Digital Library