# linear recurrence relation ?

• July 11th 2013, 04:10 PM
n22
linear recurrence relation ?
Hello,
I require some help in understanding whats going on here. THanks.
I dont understand what is the use of Un-1 ? what is meant by (n-1) please explain.
thanks.

The standard form of linear recurrence relation in vector/matrix form is Un=AUn-1, where A is kxk matrix.

Un=(xn ;yn ;zn)

and hence obtain a paticular solution
Un=AUn-1
• July 12th 2013, 12:38 AM
emakarov
Re: linear recurrence relation ?
$U_n$ is a function from natural numbers to vectors. Correspondingly, $U_{n-1}$ is the value of that function at n - 1.
• July 12th 2013, 03:29 AM
n22
Re: linear recurrence relation ?
Quote:

Originally Posted by emakarov
$U_n$ is a function from natural numbers to vectors. Correspondingly, $U_{n-1}$ is the value of that function at n - 1.

I meant ,what is (n-1) doing ? does it refer to the one before (whatever sequence it may be ?)
as opposed to (n+1),which refers to the thing after.
• July 12th 2013, 04:36 AM
emakarov
Re: linear recurrence relation ?
Quote:

Originally Posted by n22
I meant ,what is (n-1) doing ? does it refer to the one before (whatever sequence it may be ?)
as opposed to (n+1),which refers to the thing after.

Yes. But ultimately a recurrence relation is an equation containing a function U from natural numbers to something (vectors in this case). It relates the value of U at n to the values of U at arguments smaller than n.