@article{sak-kas-98-aa-allsol-tr,
  author = {Takayu Sakiyama and Masahide Kashiwagi},
  title = {An Algorithm for Finding All Solutions Using Affine Arithmetic},
  journal = {IEICE Technical Report},
  volume = {97},
  number = {532},
  pages = {49-55},
  year = 1998,
  month = feb,
  note = {In Japanese.},
  abstract = {This paper proposes a method for finding all solutions of nonlinear equations with guaranteed accuracy, which is improved by using affine arithmetic. The feature of affine arithmetic is that it keeps the correlation between variables(input and intermediate variables), unlike interval arithmetic. Affine arithmetic is superior to interval arithmetic in point of providing tighter intervals. Therefore the algorithm using affine arithmetic can remove the nonexistent regions of the solution more efficiently than using interval arithmetic. Some numerical examples show the efficiency of the proposed algorithm.}
}