Newton ’ s Method for ω - Continuous Semirings ⋆
نویسندگان
چکیده
Fixed point equations X = f (X) over ω-continuous semirings are a natural mathematical foundation of interprocedural program analysis. Generic algorithms for solving these equations are based on Kleene’s theorem, which states that the sequence 0, f (0), f (f (0)), . . . converges to the least fixed point. However, this approach is often inefficient. We report on recent work in which we extend Newton’s method, the well-known technique from numerical mathematics, to arbitrary ω-continuous semirings, and analyze its convergence speed in the real semiring.
منابع مشابه
An Extension of Newton’s Method to ω-Continuous Semirings
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)), . . . ...
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