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Math Help - Solving simultaneous recurrence relations

  1. #1
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    Cool Solving simultaneous recurrence relations

    How to start the following problem that is asking to solve simultaneous recurrence relations:
    An = 4 A(n-1) + 3 B(n-1)
    [A subscript n = 4 * A subscript (n-1) + 3 * B subscript (n-1)]
    Bn = 2 A(n-1) + 3 B(n-1)
    [B subscript n = 2* A subscript (n-1) + 3* B subscript (n-1) ]

    I know how to solve recurrence relations so I don't need help but what is confusing me is to solve simultaneous recurrence relations. How can I start?

    Thank you for your time and any type of help you can provide me!
    This is only a fictif example, so if anyone could provide me a solution, I will try to apply it to the real problem that I have to solve.
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  2. #2
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    Quote Originally Posted by precious_pearl13 View Post
    How to start the following problem that is asking to solve simultaneous recurrence relations:
    An = 4 A(n-1) + 3 B(n-1)
    [A subscript n = 4 * A subscript (n-1) + 3 * B subscript (n-1)]
    Bn = 2 A(n-1) + 3 B(n-1)
    [B subscript n = 2* A subscript (n-1) + 3* B subscript (n-1) ]

    I know how to solve recurrence relations so I don't need help but what is confusing me is to solve simultaneous recurrence relations. How can I start?

    Thank you for your time and any type of help you can provide me!
    This is only a fictif example, so if anyone could provide me a solution, I will try to apply it to the real problem that I have to solve.
    A_n = 4 A_{n-1} + 3 B_{n-1} .... (1)

    B_n = 2 A_{n-1} + 3 B_{n-1} .... (2)

    From (2): A_{n-1} = \frac{B_n - 3 B_{n-1}}{2} and it follows from this that A_{n} = \frac{B_{n+1} - 3 B_{n}}{2}.

    Substitute both these expressions into (1) and solve the resulting recurrence relation for B_n.
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