The accuracy of Taylor model methods has been shown to scale with the (n+1)-st order of the underlying domain, and as a consequence, they are particularly well suited to model functions over relatively large domains. Moreover, since Taylor models can control the cancellation and dependency problems that often affect regular interval techniques, the new method can successfully deal with complicated multidimensional problems. As an application of these new methods, a high-order extension of the standard Interval Newton method that converges approximately with the (n+1)-st order of the underlying domain is developed.
Several examples showing various aspects of the practical behavior of the methods are given.
M. Berz, J. Hoefkens, Reliable Computing 7(5) (2001) 379-398
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