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minmaxplussys

Bipartite min-max-plus system

Calling Sequence

[x] = minmaxplussys(A,B,x0)

Parameters

A
: input matrix have of size n x m .
B
: input matrix have of size m x n .
x0
: input vector have of size (m+n) x 1 .
x
: output vector have of size (m+n) x 1 .

Description

Bipartite min-max-plus system given by equations

x2 = A⊗y1 and y2 = B⊗' x1 (1)

where A∊ℝεn×m, B ∊ℝT m×n, x1,x2∊ℝεn, and y1,y2 ∊ℝT m. This function, x0=[x1;y1] and x=[x2;y2].

For details see: Subiono and J.van der Woude (2000); "Power algorithms for (max,∔)- and bipartite (min,max,∔)-systems"; DEDS, vol.10, pp.369-389, 2000.

Examples

A =[2  -3 6 2 -11;
       13 12 19 -6 21;
       -10 8 14 -5 -16];
B =[16 8 4;
       -11 10 14;
       -8 -4 4;
       13 -1 -7;
       4 7 0];

x0=zeros(8,1);
x = minmaxplussys(A,B,x0)

Author

"Min-Max-Plus Algebra And Petrinet Toolbox", ver. 2.1.0, January, 2017.

See Also


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