Oliveira, João B.João B.Oliveira2021-05-052021-05-051996-09Reliable Computing 2 (3): 299-320 (1996)http://hdl.handle.net/11420/9452This paper presents algorithms evaluating sharper bounds for interval functionsF(X) :IR n →IR. We revisit two methods that use partial derivatives of the function, and develop four other inclusion methods using the set of slopesS f (x, z) off atx εX with respect to somez εIR n. All methods can be implemented using tools that automatically evaluate gradient and slope vectors by using a forward strategy, so the complex management of reverse accumulation methods is avoided. The sharpest methods compute each component of gradients and slopes separately, by substituting each interval variable at a time. Backward methods bring no great advantage in the sharpest algorithms, since object-oriented forward implementations are easy and immediate. Fischer's acceleration scheme [2] was also tested with interval variables. This method allows the direct evaluation of the productf′(x) * (x−z) as a single real number (instead of working with two vectors) and we used it to computeF′(X) * (X−z) for an interval vectorX. We are led to decide against such acceleration when interval variables are involved. © 2021 Springer Nature Switzerland AG. Part of Springer Nature.en1573-134019963299320University of Louisiana at LafayetteInformatikMathematikJournal Article10.1007/BF02391702Other