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Math Help - linear recurrence relation ?

  1. #1
    n22
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    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
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  2. #2
    MHF Contributor
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    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.
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  3. #3
    n22
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    Re: linear recurrence relation ?

    Quote Originally Posted by emakarov View Post
    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.
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  4. #4
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    Re: linear recurrence relation ?

    Quote Originally Posted by n22 View Post
    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.
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