@inbook{heu-gri-wal-06-aa-analog,
  author = {Heupke, Wilhelm and Grimm, Christoph and Waldschmidt, Klaus},
  title = {Modeling Uncertainty in Nonlinear Analog Systems with Affine Arithmetic},
  bookTitle = {Applications of Specification and Design Languages for SoCs: Selected papers from Forum on Specification {\&} Design Languages (FDL 2005)},
  chapter = {9},
  year = 2006,
  publisher = {Springer Netherlands},
  address = {Dordrecht},
  pages = {155--169},
  isbn = {978-1-4020-4998-9},
  doi = {10.1007/978-1-4020-4998-9_9},
  comment = {Includes term reduction},
  abstract = {This chapter describes a semisymbolic method for the analysis of mixed signal systems. Aimed at control and signal-processing applications, it delivers a superset of all reachable values. The method that relies on affine arithmetic is precise for linear systems, but in the case of nonlinear systems approximations are needed. As a new term is added for each approximation, the number of approximation terms increases during simulation and therefore slows down the simulation. This leads to a quadratic time complexity in the number of time steps. A method to avoid this and an example implementation based on SystemC analog and mixed signal (AMS) are presented. Efficiency and time complexity of the improved semisymbolic simulation are analyzed and discussed.}
}