Range bounding with Taylor models: some case studies
Kyoko Makino, Martin Berz, Youn‐Kyung Kim · 2004
Abstract: Taylor model methods represent a combination of high-order multivariate automatic differentiation and the simultaneous computation of an interval remainder bound enclosing approximation error over a given domain. This method allows a far-reaching suppression of the dependency problem common to interval methods, and can thus often be used for precise range bounding problems. We compare the performance of the method with other state of the art validated tools including centered forms and mean value forms. We also compare with the computation of remainder bounds via high-order interval automatic differentiation. Key-Words: Multivariate, range bounding, interval, Taylor model, COSY Infinity.