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The Optimization Seminar is held every Tuesday from 12:00-1:30 pm in Room 626 of the CU-Denver Bldg. at the corner of Lawrence and 14th Streets (just across Speer Blvd. from the Auraria campus). Anyone with an interest in optimization is invited to attend. Refreshments are provided.
To get on our mailing list, send email to Prof. Stephen Billups.
For more information about optimization at CU-Denver, visit our
optimization community
2 0 2
A = 4 2 3
3 0 3
By iterating A^n = A A^{n-1} where matrix multiplication is done in min-plus
algebra, we get
4 2 3 6 3 5 7 5 6
A^2 = 6 3 5 A^3 = 7 5 6 A^4 = 9 6 8
4 2 3 6 3 5 7 5 6
Note A^4 = 3 A^2 (using "scalar addition") allowing us to conclude that
A^n= 3 A^(n-2) for all n >= 4. It can be shown that we can always find a
recursion with this procedure.
How long does it take to find a recursion? In many applications, the recursion is found with only a few matrix multiplications (sublinear in the matrix size). However when coefficients of a 2x2 matrix are chosen from a uniform distribution, the expected time to find a recursion is infinite.
This talk will start with an introduction to Min-Plus Algebra (with several applications) and conclude with calculations verifying the title result.
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