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Characteristics Equation

Characteristics Equation

needhelp83	15 Sep, 2009 - 12:33 PM Post #1
New D.I.C Head Joined: 11 Sep, 2009 Posts: 5	Solve the following recurrences using the characteristics equation T(n) = 4T(n-1) – 3T(n-2) T(1) = 1 T(2) = 2 T(n) – 4T(n-1) + 3T (n-2) = 0 r^n r^n-1 r^n-2 r^n – 4r^n-1 + 3r^n-2= 0 r^n-2 (r^2 -4r + 3) = 0 r = 3, r= 1 T(n) = C1 3n + C2 1n For T(1) =1 C1 3^1 + C2 1^1 = 1 For T(2)=2 C1 3^2 + C2 1^2 = 2 9C1 + C2 = 2 Solving C1 C2 = 1 - 3C1 9C1 + (1 - 3C1 ) = 2 6C1 + 1 = 2 C1 = 1/6 Solving for C2 3*(1/6) + C2 = 1 (½) + C2 = 1 C2 = ½ for T(2) = 2 C1 3^2 + C2 1^2 = 1 for T(2) = 2 Therefore: T(n) = (1/6) 3n + (½) 1n Did I do this correctly?
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Neumann	RE: Characteristics Equation 15 Sep, 2009 - 04:15 PM Post #2
I can judge a book by its cover Joined: 8 Jul, 2009 Posts: 686 Thanked: 93 times Dream Kudos: 225 My Contributions	Whoa, what the hell is r^n r^n-1 r^n-2? Where did you get that from, that's not a characteristic equation. The characteristic equation here is r^2 -4r + 3 with roots 3 and 1.
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