Max-plus algebra possible eigenvector of interval matrices
[As,lx] = maxplusposegv(A,B,x)
Function returns an possible eigenvalue lx and matrix As that satisfies
A≤As≤B, As⊗x = lx⊗x, and A⊗x ≤ As⊗x ≤ B⊗x.
And returns As=[], ls=[] if the vector x is not possible eigenvector of interval matrices. For more detailed, see: Cechlarova, K. (2005), "Eigenvectors of Interval Matrices over Max-Plus Algebra", Discrete Applied Mathematics, vol.150, 2-15.
A = [2. 6. 6. 2. 3.; 8. 8. 7. 2. 9.; 0. 7. 7. 2. 2.; 3. 9. 2. 9. 3.; 7. 1. 5. 7. 4.]; B = [3. 15. 9. 3. 7.; 16. 14. 10. 11. 12.; 5. 13. 15. 8. 7. ; 3. 16. 3. 12. 8.; 16. 4. 14. 11. 4.]; x = [6;7;9;5;3]; [As,lx]=maxplusposegv(A,B,x) // Check that A⊗x≤As⊗≤B⊗x maxplusotimes(A,x)<=maxplusotimes(As,x)&maxplusotimes(As,x)<=maxplusotimes(B,x) | ![]() | ![]() |