Find the solution to the following lhcc recurrence, confused

In summary, Tide found the constants r1 and r2 by solving for r1 and r2 in an equation that had initial conditions given.
  • #1
mr_coffee
1,629
1
ello ello!
I ran into this problem and i went in circles trying to figure it out. Anyone have any suggestions?
Here is what i have:
Find the solution to the following lhcc recurrence:
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/3c/1e4624e0fc726276872050e3ffe28d1.png [Broken]
with initial conditions http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/77/41b1266f6e87bb1b57dd6883644c521.png [Broken]

The solution is of the form: http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/b5/d7df51334509f4e8eb7c12482421651.png [Broken]
or suitable constants http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/ba/23a25f303b1dfba5efa3cc7dbfba401.png [Broken] with http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/8d/8623a3204922fa8125ce9b843a6b9b1.png [Broken]
Find these constants.
[tex]r_1 = r_2 = \alpha_1 = \alpha_2 =[/tex]

Okay so I plugged the 2 inital conditions in for the solution form and got:
1 = [tex]\alpha_1[/tex] + [tex]\alpha_2[/tex]
4 = [tex]\alpha_1[/tex]*r1 + [tex]\alpha_2[/tex]*r2

I can't solve t hat, too many unkowns and not enough equations. I also tried to find a2,a3,a4, then putting it all in terms of a0 and a1, then i was like urnt, what now? THanks!
 
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  • #2
You should have found specific values for the r's (4 and 3) before applying the initial conditions and you have a simple system of two equations and two unknowns (the alphas).
 
  • #3
Thanks for the responce Tide but I'm still alittle lost.
I usually found the R's when they gave me an equation like r^2+4r+2 = 0, then just solve for r to find r1 and r2. How did u figure out r1 = 4 and r2 = 3?
 
  • #4
Did you notice that while you used the initial conditions, you didn't use the recurrance itself anywhere? What happens if you plug
an= rn into the recurrance equation?
 

What is an LHCC recurrence?

An LHCC recurrence, or linear homogeneous constant coefficient recurrence, is a type of mathematical equation that describes the relationship between successive terms in a sequence. It is commonly used in the field of computer science and can be solved using various techniques.

How do I find the solution to an LHCC recurrence?

There are several methods for solving an LHCC recurrence, including substitution, characteristic equations, and generating functions. Depending on the specific recurrence, different methods may be more efficient or practical.

What does it mean to be "confused" when solving an LHCC recurrence?

Being "confused" in this context means that the solution to the recurrence is not immediately apparent or easy to find. It may require multiple attempts or a combination of methods to arrive at a solution.

Why is it important to find the solution to an LHCC recurrence?

LHCC recurrences are commonly used in computer science to analyze the time and space complexity of algorithms. By finding the solution, we can determine the growth rate of a sequence and make predictions about its behavior.

Are there any real-world applications for LHCC recurrences?

Yes, LHCC recurrences have various applications in fields such as computer science, engineering, and economics. For example, they can be used to analyze the performance of algorithms, model population growth, or predict stock market trends.

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