An Extension of Newton ’ s Method to ω-Continuous Semirings ?

@inproceedings{Esparza2007AnEO,
  title={An Extension of Newton ’ s Method to ω-Continuous Semirings ?},
  author={Javier Esparza and Stefan Kiefer and Michael Luttenberger},
  year={2007}
}
Fixed point equations x = F (x) over ω-continuous semirings are a natural mathematical foundation of interprocedural program analysis. Equations over the semiring of the real numbers can be solved numerically using Newton’s method. We generalize the method to any ω-continuous semiring and show that it converges faster to the least fixed point than the Kleene sequence 0, F (0), F (F (0)), . . . We prove that the Newton approximants in the semiring of languages coincide with finiteindex… CONTINUE READING

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