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Encyclopedia > Least fixed point

In mathematics, the least fixed point in order theory of a function is the fixed point which is less than or equal to all other fixed points, according to some partial order.


For example, the least fixed point of the real function

f(x) = x2

is x = 0 with the usual order on the real numbers. Many fixed-point theorems yield algorithms for locating the least fixed point. Least fixed points often have desirable properties that arbitrary fixed points do not.


  Results from FactBites:
 
least - definition of least - Labor Law Talk Dictionary (261 words)
least - used to form the superlative; "The garter snake is the least dangerous snake"
Upon the mast they saw a young man, at least if he were a man, who sat as on horseback.
Least squares (Math.), a method of deducing from a number of carefully made yet slightly discordant observations of a phenomenon the most probable values of the unknown quantities.
Fixed point (mathematics) - Wikipedia, the free encyclopedia (655 words)
In mathematics, a fixed point (sometimes shortened to fixpoint) of a function is a point that is mapped to itself by the function.
Points which come back to the same value after a finite number of iterations of the function are known as periodic points; a fixed point is a periodic point with period equal to one.
Attractive fixed points are a special case of a wider mathematical concept of attractors.
  More results at FactBites »


 

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