BUILT-IN MATHEMATICA SYMBOL

FixedPointList

generates a list giving the results of applying f repeatedly, starting with expr, until the results no longer change.

The last two elements in the list produced by FixedPointList are always the same.

FixedPointList applies SameQ to successive pairs of results to determine whether a fixed point has been reached.

FixedPointList[f, expr, ..., SameTest->s] applies s to successive pairs of results.

Find the sequence of values leading to a fixed point:

Repeated application of a rule until the result no longer changes:

Find the sequence of values leading to a fixed point:

Out[1]=

Out[2]=

Repeated application of a rule until the result no longer changes:

Out[1]=

Out[2]=

Stop after at most 5 steps:

Stop as soon as successive iterations differ by less than

:

Show convergence to

in Newton's method:

Number of steps needed to converge to a fixed point of Cos:

Matrix convergence:

Evaluate combinators:

Go up a directory tree to its root (the result will depend on computer system):

Repeated differentiation:

FixedPoint gives the last element of FixedPointList:

NestList goes for a fixed number of steps:

Apply rules repeatedly until the result no longer changes:

FixedPointList is equivalent to a particular choice of arguments of NestWhileList:

When finding a fixed point, numerical precision may increase:

The depth of intermediate expressions in a combinator evaluation []: