linear recurrence relation ?

Hello,

I require some help in understanding whats going on here. THanks.

I dont understand what is the use of U_{n-1 ? what is meant by (n-1) please explain. }thanks.

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

U_{n}=(x_{n} ;y_{n} ;z_{n)}

_{and hence obtain a paticular solution }

_{Un=AUn-1}

Re: linear recurrence relation ?

is a function from natural numbers to vectors. Correspondingly, is the value of that function at n - 1.

Re: linear recurrence relation ?

Quote:

Originally Posted by

**emakarov** is a function from natural numbers to vectors. Correspondingly,

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.

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.

You may read the Wikipedia article about recurrence relations.