论文信息 - A solution of a tropical linear vector equation

A solution of a tropical linear vector equation

A linear vector equation is considered defined in terms of idempotent mathematics. To solve the equation, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces and reduces the solution of the equation to that of a tropical optimization problem. Based on the approach, existence and uniqueness conditions are established for the solution, and a general solution to the equation is given.

Nikolai K. Krivulin

[1] Willi Hock,et al. Lecture Notes in Economics and Mathematical Systems , 1981 .

[2] Geert Jan Olsder,et al. Max Plus at Work-Modelling and Analysis of Synchronized Systems , 2006 .

[3] P. Butkovic. Max-linear Systems: Theory and Algorithms , 2010 .

[4] Geert Jan Olsder,et al. Synchronization and Linearity: An Algebra for Discrete Event Systems , 1994 .

[5] J. Golan. Semirings and Affine Equations over Them: Theory and Applications , 2003 .

[6] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.

[7] Grigori Litvinov,et al. The correspondence principle for Idempotent Calculus and some computer applications // Gunawardena , 1998 .