19.2.2. Associated Homogeneous Recurrence Relation

Try these first

1. 1.

   Define a homogeneous recurrence relation.

   Hint

   Think about equations that involve only previous terms.

2. 2.

   What is the purpose of finding a particular solution?

   Hint

   Consider how it completes the solution.

3. 3.

   What do we do first to solve a non-homogeneous recurrence equation?

   • Solve for the particular solution
   • Check initial conditions
   • Form the associated homogeneous recurrence relation

   Hint

   Recall the steps we discussed.

4. 4.

   Consider the function F(n) = n. Is this homogeneous?

   • True
   • False

   Hint

   Think about what defines a homogeneous function.

5. 5.

   Given the recurrence relation a(n) = 2a(n-1) + 3^n, what steps must be taken to solve for a(n)?

   Hint

   Focus on identifying homogeneous and non-homogeneous parts.

6. 6.

   For the relation T(n) = T(n-1) + n^k with k being a constant. What do you consider when solving it?

   Hint

   The degree of the polynomial should match the degree of F(n).