The method of Taylor models combines Taylor polynomials and remainder error enclosures, and operations are now conducted on Taylor models, where the bulk amount of the functional dependency is carried in the polynomial part, and the error enclosures provides a safety net to rigorously guarantee the result. Using simple and yet challenging benchmark problems, we demonstrate how the method works to bring those conventional difficulties under control. In the process, we also illustrate some ideas that lead to several Taylor model based algorithms and applications.
K. Makino, M. Berz, Lecture Notes in Computer Science 10381 (2017) 3-13
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