Max-Plus Algebra >> Max-Plus Algebra > maxplusposegv

maxplusposegv

max-plus algebra possible eigenvector of interval matrices

Calling Sequence

[As,lx] = maxplusposegv(A,B,x)

Parameters

A: : an input square matrix of size n by-n in
B: : an input square matrix of size n by-n
x: : an input vector dimension n
As: : an output square matrix of size n by-n such that A≤As≤B.
lx: : an outnput scalar that is an eigenvalue of matrix as.

Description

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.

Examples

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)
lx  =

  11.  
As  =

  3.     10.    8.     3.     7.   
 12.    11.    9.     11.    12.  
  5.     13.    11.    8.     7.   
  3.     9.     3.     11.    8.   
  8.     4.     5.     9.     4.   

// Check that A⊗x≤As⊗≲B⊗x
maxplusotimes(A,x) <= maxplusotimes(As,x) & maxplusotimes(As,x) <= maxplusotimes(B,x)
ans  =

T  
T  
T  
T  
T

Author

Subiono

"Max-Plus Algebra Toolbox", ver. 1.01, April, 2009.