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FixedPoint

FixedPoint
starts with expr, then applies f repeatedly until the result no longer changes.
  • FixedPoint always returns the last result it gets.
  • FixedPoint applies SameQ to successive pairs of results to determine whether a fixed point has been reached.
Find a value such that :
Fixed point of an integer-valued function:
Repeated application of a rule until the result no longer changes:
Find a value such that :
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Fixed point of an integer-valued function:
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Repeated application of a rule until the result no longer changes:
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Numerical fixed point of a function:
Fixed point of a repeated transformation:
Stop after at most 10 steps:
Stop as soon as successive iterations differ by less than :
Perform exact arithmetic, but use a numerical comparison function:
Find using Newton's method:
Fixed point of a complex iteration:
Matrix-multiplication convergence:
Root of the current directory tree (the result will depend on computer system):
Repeated differentiation:
Find the minimum of with the steepest-descent method (vector notation):
Component notation:
Evaluate combinators []:
Connected components in a graph:
FixedPoint gives the last element of FixedPointList:
Apply rules repeatedly until the result no longer changes using ReplaceRepeated (//.):
FixedPoint is equivalent to a particular choice of arguments of NestWhile:
Calculations may not converge in a finite number of steps:
Providing a maximum number of iterations will guarantee termination:
Using a numerical test for convergence works in this case as well:
Sometimes convergence may fail on certain platforms due to insufficient accuracy of a machine arithmetic library function. This can be addressed by using a comparison function with a larger tolerance:
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