A closed form function which gives the value of a sequence at index has only one parameter, itself. This is in contrast to the recurrence relation form, which can have all of the previous values of the sequence as parameters.
The benefit of the closed form is that one does not have to calculate all of the previous values of the sequence to get the next value. This is not too useful if one wants to print out or utilize all of the values of a sequence up to some , but it is very useful to get the value of the sequence just at some index .
There are many techniques used to find a closed-form solution for a recurrence relation. Some are
Repeated substitution. Replace each in the expression of (with ) with its recurrence relation representation. Repeat again on the resulting expression, until some pattern is evident.
|Date of creation||2013-03-22 11:56:10|
|Last modified on||2013-03-22 11:56:10|
|Last modified by||akrowne (2)|